## Choose a sublist of interest

- Arithmetic Geometry
- ag.algebraic-geometry nt.number-theory
- Topology
- at.algebraic-topology gt.geometric-topology

## Or choose your own subject tags below

Welcome to MathMeetings.net! This is a list for research mathematics conferences, workshops, summer schools, etc.

There are a few other conference lists available, but this list
aims to be more complete by allowing *anyone at all* to add
announcements. Rather than use a wiki, announcement information is
stored in database format so that useful search functions can be
added as the list grows.

This site began as AlgTop-Conf, for meetings in algebraic topology. It is now expanded to serve other mathematics subjects. Use tag filtering to focus on announcements related to your discipline (see right or below).

## Know of a meeting not listed here? Add it now!

#### Updates 2016-01

- Now filter announcements by subject tags
- Form for editing announcements is now the same as that for adding new announcements
- New 'view' page for each announcement, and announcement data in confirmation emails
- Select boxes improved with select2 (jquery)

Additional update notes are available in the git repository (GitHub).

# Upcoming Meetings

## January 2017

### Unlikely Intersections, Heights, And Efficient Congruencing

Meeting Type: long-term research program

Contact: see conference website

### Description

In recent years there has been a great deal of success in applying methods of analytic number theory to questions of arithmetic geometry. This conference will focus on three topics: o-minimality, heights, and "efficient congruencing". The first two topics have been very useful in attacking conjectures regarding "special" points such as the Andre-Oort conjecture, or more generally the Zilber-Pink conjecture, while the third establishes the Hasse principle for certain varieties associated with translation-dilation invariant systems at the threshold of the convexity barrier.

This program will include several conferences, to be posted separately.

### Analytic Number Theory

Meeting Type: long-term research program

Contact: see conference website

### Description

Analytic number theory, and its applications and interactions, are currently experiencing intensive progress, in sometimes unexpected directions. In recent years, many important classical questions have seen spectacular advances based on new techniques; conversely, methods developed in analytic number theory have led to the solution of striking problems in other fields.

Recent advances in analytic number theory have had repercussions in various mathematical subjects, such as harmonic analysis (including the Langlands programme), ergodic theory and dynamics (especially on homogenous spaces), additive and multiplicative combinatorics and theoretical computer science (in particular, through the theory of expander graphs).

The MSRI semester program in Spring 2017 will focus on the topic of Analytic Number Theory, with workshops and other activities focused on the most impressive recent achievements in this field. We wish not only to give the leading researchers in the area further opportunities to work together, but more importantly to give young people the occasion to learn about these topics, and to give them the tools to achieve the next breakthroughs.

This program includes several conferences, to be posted separately.

## April 2017

### Special Trimester on Representation Theory of Reductive Groups Over Local Fields and Applications to Automorphic forms

Meeting Type: Special trimester

Contact: Dmitry Gourevitch, Avraham Aizenbud, Erez Lapid, Joseph Bernstein

### Description

## May 2017

### K-Theory and Related Fields

Meeting Type: long-term research program

Contact: see conference website

### Description

Mathematicians from many areas are interested in K-theory, and they all look at it from their own perspective. The program modestly plans to support research in several of the many sub-areas of K-theory and to promote synergies between the different, but often overlapping, areas. The program will involve the following elements:

A summer school directed at PhD students and young postdocs, scheduled for the week June 19 - June 23.

Three major workshops, as follows:

```
K-theory in algebraic geometry and number theory, May 15 - May 19,
K-theory and related fields, June 26 - June 30,
K-theory in topology and non commutative geometry, August 21 - August 25.
```

Informal short courses and learning seminars, in between the major workshops, to help those working in one aspect of K-theory learn about developments and techniques in other areas.

### Modular Forms are Everywhere

Meeting Type: conference

Contact: see conference website

### Description

### Harmonic Analysis and the Trace Formula

Meeting Type: invitational conference

Contact: see conference website

### Description

```
Organisers
```

Werner Müller, Bonn

Sug Woo Shin, Berkeley

Birgit Speh, Ithaca

Nicolas Templier, Ithaca

### BIT’s 8th Annual World Congress of Neurotalk-2017

Meeting Type: conference

Contact: Anna Song

### Description

Welcome The Annual World Congress of Neurotalk (NT), initiated from 2010, had been successfully organized in Singapore, Dalian, Beijing, Xi'an, Nanjing，Hangzhou and Beijing again, attracted more than 5,000 participants from 60 countries. Neurotalk series congresses contribute to offering professionals in the field of Neuroscience a multidisciplinary informative cooperative platform, and it has been the most definite and grand Neuroscience event in Asia.

The Neurotalk-2017, with the theme of "New Technologies, New Ideas and New Future" will be held on May 22-24, 2017 in Barcelona, Spain.

We hope your participation would contribute to your professional development and relationships. Wish you enjoy the conference.

### Georgia International Topology Conference

Meeting Type: conference

Contact: see conference website

### Description

This is the eighth installment of a major conference in geometric topology and related areas that has been held at the University of Georgia every eight years since 1961. The 2017 conference will include dozens of speakers whose ideas have advanced the field over the last several years. Over two weeks, the conference will provide plenty of time for collaboration and for interaction between junior and senior researchers.

We have significant funding available to support the participation of graduate students and early-career mathematicians; those interested, especially from underrepresented groups, should apply at the conference website.

### Arithmetic Aspects of Explicit Moduli Problems

Meeting Type: conference

Contact: Nils Bruin, Kiran Kedlaya, Samir Siksek, John Voight

### Description

Explicit work on moduli problems has yielded powerful new theorems in arithmetic geometry that have eluded a purely theoretical approach. The moduli approach converts the problem of classifying objects of arithmetic interest into the problem of studying rational points on varieties, to which the methods of algebraic and arithmetic geometry may be applied. There is an active community, including many young researchers, dedicated to explicitly studying rational points. This workshop will bring together researchers working on explicit moduli problems with those working on rational points to establish collaborations and stimulate further research.

In addition to providing a platform for communicating new developments, the workshop will give young researchers the opportunity to gain a strong foundation in moduli spaces going beyond those traditionally studied computationally.

### Higgs bundles and related topics

Meeting Type: conference

Contact: see conference website

### Description

The conference aims at bringing together researchers working in the numerous fields involving Higgs bundles and giving account on recent progress made in topics like the geometry and topology of their moduli spaces, Teichmüller theory, surface group representations and non-abelian Hodge theory. We plan to have a rather limited number of talks and leave space for informal discussions.

Here is the list of the speakers which have confirmed so far:

Jorgen Andersen David Baraglia Indranil Biswas Tsao-Hsien Chen David Dumas Vladimir Fock Tamas Hausel Victoria Hoskins Adrian Langer Qiongling Li Marina Logares Takuro Mochizuki Motohico Mulase Pranav Pandit Laura Schaposnik Richard Wentworth Kang Zuo

Limited financial support is available, especially for PhD students and Post-Docs who are strongly encouraged to apply. We kindly ask you to forward the present announcement to your colleagues.

The scientific committee

François Labourie Christian Pauly Carlos Simpson

### Princeton-Rider Workshop on the Homotopy Theory of Polyhedral Products

Meeting Type: conference

Contact: Tony Bahri

### Description

Cartesian products have embedded within them certain natural subsets which are indexed by combinatorial information. The geometric characterization of these subspaces, known now as polyhedral products, has application in toric geometry and topology, combinatorics,geometric group theory, number theory, homotopy theory and arachnid mechanisms. The workshop will focus on the topology and geometry of these and related spaces.

### Artin L-functions, Artin's primitive roots conjecture and applications a CIMPA-ICTP research school

Meeting Type: CIMPA-ICTP research school

Contact: Valerio Talamanca

### Description

This school is intended to foster analytic number theory as well as algebraic number theory and arithmetic geometry in Turkey and neighbouring countries. The school revolves around Artin's primitive root conjectures and Artin's L-functions, two subjects that lie at the crossroads of these three fields. It will give the attendees the opportunity to learn some basics notions on the following topics: a brief introduction to algebraic number theory culminating in the celebrated Chebotarev Density Theorem; an introduction to the representation theory of finite groups culminating in the definition of Artin's L-functions and the group theoretic proof of their meromorphicity; an introduction to zeta functions and L-functions; distribution of primes; an introduction to elliptic curves and analogues of Artin's Conjecture, and last but not least Hooley's Theorem and quasi resolution. All courses will be taught in English.

## June 2017

### N^3 Days VI

Meeting Type: conference

Contact: Lars Halvard Halle, Fabien Pazuki, Sho Tanimoto

### Description

See the website

### Mathematics Research Communities: Homotopy Type Theory

Meeting Type: MRC workshop

Contact: Chris Kapulkin

### Description

### Numeration2017

Meeting Type: conference

Contact: Valerio Talamanca

### Description

**The goal of this workshop is to bring together researchers interested in interactions between numeration systems, ergodic theory, number theory and combinatorics.**

Conference Topics

General numeration systems Geometric representations, Rauzy fractals, tilings Representations of operations in Pisot base by finite automata Sofic systems associated with Pisot numbers Redundant representations and cryptography Shift-radix systems Abstract number systems Beta-integers and their combinatorial properties Spectra and spectral measures associated with numeration Sums of digits for classical and non-classical numerations, associated fractals Analytic and probabilistic study of arithmetic functions related to numeration Combinatorics on words and Diophantine approximation Algebraic and transcendental numbers linked with beta-numeration

### P-adic Hodge Theory and Automorphic Forms

Meeting Type: conference

Contact: see conference website

### Description

This workshop will focus on recent developments in p-adic Hodge theory and automorphic forms, especially their interplay.

### PIMS-CRM Summer School in Probability 2017

Meeting Type: conference

Contact: Omer Angel

### Description

There will be two main courses lasting for the entire school, and three mini-courses, one on each of the first three weeks.

Marek Biskup: Level sets and extreme points of the Discrete Gaussian Free Field and related processes.

The Gaussian free field (GFF) is a fundamental model for random fluctuations of a surface. The GFF is closely related to local times of random walks via relations that originated in the study of spin systems. The continuous GFF appears as the limit law of height functions of dimer covers, uniform spanning trees and other models without apparent Gaussian correlation structure. The GFF is also a simple example of a quantum field theory. Intriguing connections to SLE, the Brownian map and other recently studied problems exist.

The GFF has recently become subject of focused interest by probabilists. Through Kahane's theory of multiplicative chaos, the GFF naturally enters into models of Liouville quantum gravity. Multiplicative chaos is also central to the description of level sets where the GFF takes values proportional to its maximum, or values order-unity away from the absolute maximum. Random walks in random environments given as exponentials of the GFF show intriguing subdiffusive behavior. Universality of these conclusions for other models such as gradient systems and/or local times of random walks are within reach.

Hugo Duminil-Copin: Graphical approach to lattice spin models.

Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids (lattice gases).

It has been understood since the 1980s that random geometric representations, such as the random walk and random current representations, are powerful tools to understand spin models. In addition to techniques intrinsic to spin models, such representations provide access to rich ideas from percolation theory. In recent years, for two-dimensional spin models, these ideas have been further combined with ideas from discrete complex analysis. Spectacular results obtained through these connections include the proof that interfaces of the two-dimensional Ising model have conformally invariant scaling limits given by SLE curves, that the connective constant of the self-avoiding walk on the hexagonal lattice is given by √ 2 + √ 2 , and that the magnetisation of the three-dimensional Ising model vanishes at the critical point.

Mini-courses:

Christina Goldschmidt: Scaling limits of random graphs.

Martin Hairer: A BPHZ theorem for stochastic PDEs.

Sandra Cerrai: On some asymptotic problems for stochastic PDEs.

### Journées Algophantiennes Bordelaises 2017

Meeting Type: conference

Contact: see conference website

### Description

The conference will be dedicated to algorithmic solutions of Diophantine equations. This rapidly developping field experienced remarkable progress during the last years. Novel methods were introduced and new spectacular applications were given, the proof of the modularity conjecture over real quadratic field being a notable example.

The invited speakers include

```
Nuno Freitas* (Vancouver)
Rafael von Känel (Princeton)
Hendrik W. Lenstra (Leiden)
Jean-François Mestre (Paris VII)
Samir Siksek (Warwick)
Michael Stoll (Bayreut)
```

### European Talbot 2017: Dualities in Algebra, Geometry, and Topology

Meeting Type: workshop

Contact: Bertram Arnold, Tobias Barthel, Magdalena Kedziorek, and Sean Tilson

### Description

The third European Talbot workshop will take place in Germany from June 11 to June 17, 2017. The goal is to bring together a group of 30-35 graduate students and post-docs to work on a focused topic under the guidance of two senior mentors.

This years topic is "Dualities in Algebra, Geometry, and Topology" and is mentored by John Greenlees and Mike Hill. More information can be found at the workshops website website.

### Meeting of the Catalan, Spanish, Swedish Math Societies, special session in homotopy theory

Meeting Type: special session

Contact: Tilman Bauer, Natalia Castellana

### Description

**Meeting of the Catalan, Spanish, Swedish Math Societies
(CAT-SP-SW-MATH)**

A joint Meeting of the Catalan, Spanish, Swedish Math Societies (CAT-SP-SW-MATH) will be held in Umeå (Sweden) from 12th to 15th June 2017.

The meeting is a symposium devoted to mathematics at large. The conference is thought as a meeting point between the different areas of mathematics and its applications.

The programme will consist of several plenary lectures, covering a wide range of areas of mathematics, and special sessions devoted to a single topic or area of mathematics.

There is going to be a special session in homotopy theory, chaired by Natalia Castellana and Tilman Bauer, with the following speakers:

Alexander Berglund: Rational homotopy theory of automorphisms of manifolds Federico Cantero: Rational homotopy theory of Thom spaces Cristina Costoya: Polyhedral products in Kahn’s Realizability Problem Felix Wierstra: Hopf invariants in rational homotopy theory Kiko Belchí: Persistent homology: from Stasheff to the hospital Antonio Viruel: On the realizability of group actions Albert Ruiz: On the classification of p-local compact groups over a fixed dis- crete p-toral group Magnus Carlson: Higher obstructions to the embedding problem in Galois theory Carlos Sáez:Finite subgroups of diffeomorphisms of 4-manifolds Thomas Kragh: Waldhausens K-theory of spaces and exact Lagrangian submanifolds Ramón Flores: Burnside groups and idempotent transformations of groups

Everybody is welcome to attend, whether Catalan-Spanish-Swedish or not.

### L-Functions and Modular Forms Database

Meeting Type: software development workshop

Contact: see conference website

### Description

This workshop is one of a series during which development will take place on the LMFDB (L-functions and Modular Forms Database) project. As usual with workshops in this series, there will be few lectures with most of the time devoted to LMFDB-related work and development. We will have discussions on general LMFDB development and future plans, as well as the main focus of activity which will be on classical, Hilbert and Bianchi modular forms and their L-functions, and Galois representations.

### Arakelov geometry and diophantine applications

Meeting Type: Summer School

Contact: Huayi Chen, Emmanuel Peyre, Gaël Rémond

### Description

Main Speakers:

- Fabrizio Andreatta
- Pascal Autissier
- Jean-Benoît Bost
- Jan Bruinier
- José Ignacio Burgos Gil
- Antoine Chambert-Loir
- Huayi Chen
- Romain Dujardin
- Gerard Freixas i Montplet
- Éric Gaudron
- Emmanuel Peyre
- Per Salberger
- Christophe Soulé

### Groups, Rings and the Yang-Baxter Equation

Meeting Type: international conference

Contact: Doryan Temmerman

### Description

A conference about "Groups, Rings and the Yang-Baxter equation" will be held at Domain Sol Cress in the beautiful town of Spa, Belgium. The international conference focusses on recent developments in the areas of ring theory, group theory and the new structure, called braces, that recently has attracted a lot of attention because of its role in a description of set-theoretic solutions of the Yang-Baxter equation. Special emphasis is given on the relations between these areas and in particular on topics where a mixture of methods (involving these theories) has been used. Some topics of particular interest are: group rings, unit groups, (graded) rings and also various algebraic structures used in the context of the Yang-Baxter Equation.

### Arithmetic, Geometry, Cryptography and Coding Theory

Meeting Type: conference

Contact: see conference website

### Description

We wish to organize a conference involving the interactions between theoretical mathematics, as number theory and algebraic geometry, with information theory and communication, as coding theory and cryptography. This conference would be the sixteenth edition of a conference which began in 1987 with the best specialists of the field. The students and young researchers are also invited to collaborate with seniors researchers.

The talks will concern new theoretical mathematical results but also presentation of effective or algorithmic results. The conference will be on a week (five days) with the following schedule : — One or two plenary talks each day at the beginning of the session given by high level researchers. Our hope is that a part of these talks will be given by researchers not in our community in order to present new directions and new applications of arithmetic and/or algebraic geometry. — The other talks will be specialized short ones.

At the end of the conference, we plan to publish proceedings in the Contemporary Mathematics collection of the AMS.

Topics of the Conference — Number theory, asymptotic behavior of families of global fields and statistic arithmetic. — Arithmetic geometry, algebraic curves over finite fields or over number fields, Abelian varieties : point counting methods, theoretical, effective and algorithmic aspects in arithmetic geometry. — Error correcting codes, algebraic codes, geometric codes on algebraic curves or on high dimensional varieties, algebraic decoding algorithms, etc. — Cryptography, elliptic curves and Abelian varieties : discrete logarithm problem, pairings, explicit computing of isognies, invariant theory and curves classification. — Boolean functions, bent functions, APN functions : construction of families of bent functions and hyperbent functions, etc.

### Dynamics, aging and universality in complex systems: A celebration in honor of Gérard Ben Arous

Meeting Type: conference

Contact: Ivan Corwin

### Description

The conference has 30 confirmed speakers in very active and fundamental areas at the intersection of probability, analysis, and mathematical physics. The main aim in the rigorous study of complex disordered systems is to understand how random microscopic systems display predictable and statistically universal collective macroscopic behaviors. Many such systems evolve to stationary states, but do so in very long time scales (e.g., exponential in system size). Dynamics and aging in these complex systems seeks to understand how their complicated energy landscapes governs their pre-stationary behavior. There are many different approaches in this area that will be represented at the conference, including spin-glasses, stochastic partial differential equations (PDEs), large deviation theory, and random matrix theory.

Many of the complex systems which will be discussed in this conference aim to describe real world phenomena and results proved for the mathematical models provide predictions applicable to the real systems. At a simpler level, think, for instance, of how the central limit theorem for sums of independent random variables predicts the Gaussian statistics which drives a large part of statistics in the real world. Besides physical applications, complex systems (e.g., spin glasses, growth processes and random matrices) have found many applications in computer science, machine learning, data science, bioinformatics, chemistry, and even areas like ecology and earth science.

The speakers are:

Erwin Bolthausen, Zurich

Anton Bovier, Bonn

Jiri Cerny, Vienna

Francis Comets, Paris

Percy Deift, NYU

Amir Dembo, Stanford

Jean-Dominique Deuschel, Berlin

Persi Diaconis, Stanford

Alexander Fribergh, Montréal

Martin Hairer, Warwick

Takashi Kumagai, Kyoto

Jean-François Le Gall, Orsay

Yves Le Jan, Orsay

Eyal Lubetzky, NYU

Terry Lyons, Oxford

Sylvie Méléard, Paris

Charles M. Newman, NYU

Stefano Olla, Paris

Houman Owhadi, Caltech

Sandrine Péché, Paris

Yuval Peres, Microsoft

Jeremy Quastel, Toronto

Scott Sheffield, MIT

Vladas Sidoravicius, NYU Shanghai

Alain-Sol Sznitman, ETHZ

S.R.Srinivasa Varadhan, NYU

Wendelin Werner, ETHZ

Horng-Tzer Yau, Harvard

Ofer Zeitouni, Courant-Weizmann

### New Trends in Representation Theory: The Impact of Cluster Theory in Representation Theory.

Meeting Type: research school

Contact: Karin Baur, Sibylle Schroll

### Description

There will be a LMS-CMI Research School, 18-23 June 2017, at the University of Leicester, UK on `New Trends in Representation Theory: The Impact of Cluster Theory in Representation Theory’ organised by Karin Baur (Graz) and Sibylle Schroll (Leicester).

The school will consist of three lecture courses:

n-representation theory - Peter Jorgensen (Newcastle), Integrable systems and friezes - Sophie Morier-Genoud (Paris) infinite dimensional representations - Lidia Angeleri-Huegel (Verona)

with guest lectures by Martin Herschend (Uppsala), Pierre-Guy Plamondon (Orsay) and Mike Prest (Manchester).

More details and for registration please see: https://sites.google.com/site/clustertheoryinreptheory/home

### Workshop on O-minimality and Diophantine Applications

Meeting Type: conference

Contact: see conference website

### Description

### Arithmetic of Function Fields

Meeting Type: conference

Contact: U. Hartl, E.-U. Gekeler, A. El-Guindy, M. Papikian, A. Pál

### Description

The emphasis of the conference will be on recent spectacular developments in the Arithmetic of Function Fields, in particular, the theory of Drinfeld moduli spaces, Drinfeld modular forms, their generalizations and their applications.

### Applied Topology in Bedlewo

Meeting Type: conference

Contact: Zbigniew Błaszczyk

### Description

This will be the second edition of a conference that took place in Bedlewo in July 2013.

Similarly as before, our aim is to bring together scientists from all over the world working in various fields of applied topology, including:

- topological robotics,
- topological methods in combinatorics,
- random topology,

as well as topological data analysis, with emphasis on:

- neurotopology,
- materials analysis,
- computational geometry, and
- multidimensional persistence.

### Algebraic Analysis and Representation Theory -- In horor of Professor Masaki Kashiwara's 70th Birthday

Meeting Type: conference

Contact: see conference website

### Description

### Algebraic Topology and Representation Theory

Meeting Type: conference

Contact: Ivo Dell'Ambrogio, Antoine Touzé

### Description

The goal of this conference is to gather algebraic topologists and representation theorists around common algebraic interests, such as: group (co)homology, Hopf algebras, equivariant theories, support varieties, functorial and higher categorical methods.

To facilitate interactions between people of different backgrounds, the conference will be enriched by two mini-courses, one more oriented towards algebraic topology and the other towards representation theory.

### GAeL (Géométrie Algébrique en Liberté)

Meeting Type: workshop

Contact: see conference website

### Description

"Géométrie Algébrique en Liberté" is a conference organized by and for researchers in Algebraic Geometry at the beginning of their scientific career. The conference gives PhD students and post-docs the opportunity to lecture, often for the first time, in front of an international audience. In addition, selected international experts deliver mini-courses on topics at the cutting-edge of important new developments in Algebraic Geometry.

The senior speakers will be:

Arend Bayer (University of Edinburgh), Stability conditions and classical algebraic geometry

Angela Gibney (University of Georgia), Vector bundles of conformal blocks on the moduli space of curves

Alessandra Sarti (Université de Poitiers), Hyperkähler Manifolds

Accommodation for supported participants will be provided from 25th June to 30th June 2017. Without any promise, you can apply for the reimbursements of your travel costs if you are not supported by your university.

### Geometry of Singularities and Differential Equations

Meeting Type: conference

Contact: see conference website

### Description

The Conference is devoted to honor Prof. Felipe Cano in occasion of his 60th birthday. The aim is to present recent developments in his main research topics, all of which share a common perspective inscribed in the study of singularities of algebraic varieties and of differential equations:

```
Resolution of singularities in any characteristic.
Reduction of singularities of holomorphic codimension one foliations.
Valuations and uniformization of vector fields.
Real analytic, subanalytic and o-minimal geometry.
Geometry of trajectories and local topological dynamics of real analytic vector fields.
Invariant hypersurfaces of holomorphic codimension one foliations.
Parabolic curves of holomorphic diffeomorphisms.
Formal invariant curves and summation processes.
```

Santander is a port city in the north of Spain, the capital of Cantabria, a region which shares beach and natural landscapes. It is a rich city and a tourist destination, with remarkable landmarks and a fine set of beaches. The weather in June is mild and especially attractive in sunny days.

### Non-archimedean geometry, motives and vanishing cycles

Meeting Type: conference

Contact: see conference website

### Description

### Stable homotopy theory and p-adic Hodge theory

Meeting Type: Masterclass

Contact: Ryo Horiuchi, Martin Speirs, Lars Hesselholt

### Description

Stable Homotopy theory and arithmetic geometry are two very active areas of research today. Our speakers, Thomas Nikolaus and Matthew Morrow represent two researchers at the forefront of these areas, working in different but overlapping fields. The overall motivation for this masterclass is to study the relations between these two areas of research.

In recent years stable homotopy theory has seen unexpected applications to arithmetic geometry. In particular the work of Matthew Morrow (in collaboration with Bhargav Bhatt and Peter Scholze) on integral p-adic Hodge theory was, in part, motivated by calculations of topological Hochschild homology for certain arithmetically important rings. Very recently Lars Hesselholt has used the cyclotomic structure on topological Hochschild homology to define a topological version of periodic cyclic homology and used it to give cohomological interpretations of zeta functions for schemes over finite fields. This was in part motivated by new perspectives and results on cyclotomic structures afforded by work of Thomas Nikolaus (in collaboration with Peter Scholze).

The goal of this masterclass is to study this recent progress. In particular we will focus on the work by Nikolaus and Scholze on cyclotomic spectra and the work by Bhatt, Morrow and Scholze giving integral relations between p-adic cohomology theories. The masterclass will consist of two lecture series by Matthew Morrow and Thomas Nikolaus as well as several discussion sessions.

### PCMI Summer School: Random Matrices

Meeting Type: conference

Contact: Ivan Corwin

### Description

Organizers: Alexei Borodin (MIT), Ivan Corwin (Columbia), and Alice Guionnet (CNRS-ENS Lyon)

Lecturers: Percy Deift (New York University), Ioana Dumitriu (University of Washington), Laszlo Erdos (Institute of Science and Technology Austria), Yan Fyodorov (Queen Mary University of London), Jeremy Quastel (University of Toronto), Mark Rudelson (University of Michigan), Sylvia Serfaty (Université Pierre et Marie Curie Paris 6), Dimitri Shlyakhtenko (University of California, Los Angeles), Terence Tao (University of California, Los Angeles), and Balint Virag (University of Toronto)

Clay Senior Scholars-in-Residence: Craig Tracy (University of California, Davis), H.T. Yau (Harvard University)

Random matrix theory sits at the interface of many fields of mathematics and physics, as well as has practical applications in areas of computer science and statistics. The purpose of this school is to provide an introduction (through mini-courses and research talks) to many exciting areas of recent research in and around random matrix theory.

The topics covered in the school will include:

Universality of spectral statistics

High dimensional geometry and concentration methods

Free probability

Kardar-Parisi-Zhang universality class

Orthogonal polynomials, Riemann-Hilbert Problems and Painleve transcendents

Applications of random matrices in statistical physics, including spin-glasses

Numerical analysis of random matrices

Topological recursions and random maps

Random tilings

Random matrices and analytic number theory

### Arithmetic Geometry and Computer Algebra

Meeting Type: workshop

Contact: Jan Steffen Müller

### Description

## July 2017

### Euler Systems and Special Values of L-functions

Meeting Type: semester program

Contact: see conference website

### Description

The goal of this semester-long program is to gather the leading experts in the area of Euler systems and the Birch and Swinnerton-Dyer conjecture in order to initiate a more systematic study of Euler systems on higher rank reductive groups and their applications to generalizations of the BSD conjecture (Bloch–Kato–Beilinson conjectures). At the same time, we envision several introductory courses suitable for graduate students and post-doctoral assistants.

### Diophantine Approximation and Algebraic Curves

Meeting Type: conference

Contact: see conference website

### Description

The main objectives of the proposed conference on Diophantine approximation and algebraic curves will be the study of rational and integral solutions to Diophantine equations and inequalities and the connection with algebraic curves. Since early last century and even before, Diophantine approximation has played a large role in the study of solutions to Diophantine equations, a very old and influential topic in number theory. Thue's famous theorem was subsequently refined and expanded upon, culminating in Roth's celebrated result and his winning of the Fields medal. Shortly after that, Baker's ``effective" methods (earning him a Fields medal) were added into the mix. Concurrently with all this, the more systematic and algebraic development of the theory of curves (as opposed to the more ad hoc methods employed previously) was championed by the likes of Artin, Chevalley and Weil. A great achievement here was Falting's famous proof of Mordell's conjecture (yet another Fields medal for these areas).

Clearly these topics have intrigued mathematicians for a very long time. The techniques applied have been varied, but machinery originating here has also found use in a wide variety of fields. To mention just one example, it was noted over a century ago that the theories being developed over the rational number field applied equally well to fields of transcendence degree one over a finite field ("function fields"). Now curves defined over finite fields and their corresponding function fields are a cornerstone of modern computer coding theory.

During the proposed conference, experts in the areas of linear forms in logarithms, heights, the subspace theorem, the connections between Diophantine approximation and Nevanlinna theory, and others will come together with those in elliptic curves, abelian varieties and other closely related subjects in algebraic geometry. It is hoped that new light may be shed and insight gained into questions such as the existence of elliptic curves of large rank, the complete solution to certain families of equations, and deeper connections between the approximation of algebraic numbers and algebraic properties of curves and surfaces.

### Rational Points 2017

Meeting Type: conference

Contact: see conference website

### Description

This workshop is the sixth in a series that started with the workshops Rational Points on Curves - Explicit Methods and Rational Points on Curves and Higher-Dimensional Varieties: Theory and Explicit Methods held in 2005 and 2007 in Bremen, followed by the workshops Rational Points 3 and Rational Points 2013 in Thurnau in 2010 and 2013 and thw workshop Rational Points 2015 in Schney.

In the tradition of the earlier events, this workshop aims at bringing together the leading experts in the field, covering a broad spectrum reaching from the more theoretically-oriented over the explicit to the algorithmic aspects. The fundamental problem motivating the workshop asks for a description of the set of rational points X(Q) for a given algebraic variety X defined over Q. When X is a curve, the structure of this set is known, and the most interesting question is how to determine it explicitly for a given curve. When X is higher-dimensional, much less is known about the structure of X(Q), even when X is a surface. So here the open questions are much more basic for our understanding of the situation, and on the algorithmic side, the focus is on trying to decide if a given variety does have any rational point at all. Aim

By bringing together the leading experts and giving them the opportunity to present their latest results and their view on the field in general, we hope to provide a fertile basis for animated discussions. As a result, we hope to achieve a better understanding of the current state of the art and, more importantly, to identify and explore the most promising directions for future work. Format

This is a workshop with about 50 participants. Participation is by invitation. Every participant is expected to contribute actively to the success of the event, by giving talks and/or by taking part in the discussions. There will be two invited talks every morning (9:30-10:30 and 11:15-12:15); the afternoons will be available for shorter invited talks, discussions, informal talks and collaboration. Wednesday afternoon is free.

### Journées Arithmétiques 2017

Meeting Type: conference

Contact: Bruno Deschamps

### Description

### Persistent Homology Summer School

Meeting Type: Summer School

Contact: My Ismail Mamouni

### Description

The Persistent Homology is a recent and immersive research areas. It is a homology theory adapted in an algorithmic context to the topological data analysis. It keeps track of the homology classes that still remain "persistent" when approaching a topological space by a cloud of points. The persistent homology finds applications in all research areas that involve big datas, including medicine, chemistry, music, linguistics, sports, economics, social sciences, ....

```
The course is intended to PhD students who have already started research in Persistent homology, it can also inspire students at the end of their master to start their research in this area and finally it can interest senior and junior researchers for a re-conversion in another field of research
We plan to schedule 16 hours of courses, 6 hours of open discussion, 3 hours of Lab sessions, and 3 hours of research contributed talks.
```

### SSiEG - Summer School in Enumerative Geometry

Meeting Type: Summer School

Contact: see conference website

### Description

Chiu-Chu Melissa Liu - Columbia University

Course title: Gromov-Witten invariants, Fan-Jarvis-Ruan-Witten invariants, and Mixed-Spin-P fields

Cristina Manolache - Imperial College London

Course title: Boundary contributions to enumerative invariants

General description and aims of the school:

Gromov-Witten invariants, which "count" curves (with appropriate extra conditions) on smooth projective varieties, were introduced more than two decades ago; motivated by high energy physics, they ended up revolutionising enumerative algebraic geometry and provided a bridge to other branches of mathematics, such as integrable systems of differential equations.

Since then, their scope has been expanded in different directions (e.g. relaxing the smoothness conditions, replacing the variety by a stack, allowing torus actions), and techniques have been introduced for their computation; moreover, a plethora of other invariants using the same basic ideas has been introduced, leading to fruitful investigations on the relationships among them.

The aim of this school is to bring doctoral students, postdocs, and anyone interested from a review of the basic construction to current, state-of-the art research in this field, with a special focus on invariants for Calabi-Yau threefolds, the richest example both in algebraic geometry and in physics. Many important questions about these varieties are still unanswered, such as giving a mathematically rigorous definition of the Gopakumar-Vafa invariants (at the moment only available in the language of theoretical physics).

ORGANIZING COMMITTEE:

```
Valentina Beorchia, Trieste
Ada Boralevi, Sissa Trieste
Barbara Fantechi, Sissa Trieste
```

### Young Topologists Meeting

Meeting Type: conference

Contact: Ben Ward

### Description

The 2017 Young Topologists Meeting will take place in Stockholm from the 3rd to the 7th of July, hosted by KTH and Stockholm University. The conference will be an opportunity for graduate students, recent PhDs and other junior researchers to meet and present their work to each other. In addition to the talks given by the participants, there will be two mini-courses given by Benson Farb (University of Chicago) and Brooke Shipley (University of Illinois at Chicago).

For further information see: www.math-stockholm.se/konferenser-och-akti/young-topologists-meeting-2017-1.670396

Registration will open the 27th of January. We will be able to cover accomodation for approximately 100 participants. In addition, we are applying for NSF funding to cover travel expenses for participants from US institutions.

The Young Topologists Meeting 2017 is made possible by the generous support of:

- The Foundation Compositio Mathematica
- Stockholm Mathematics Centre

### Workshop on computational number theory

Meeting Type: conference

Contact: see conference website

### Description

### Representation theory of p-adic groups

Meeting Type: Workshop and Conference

Contact: Manish Mishra

### Description

### Fields Institute Summer School in Geometric Analysis

Meeting Type: Summer School

Contact: Spiro Karigiannis

### Description

The summer school is intended for graduate students, postdoctoral fellows, and early career researchers to learn about various fundamental topics in geometric analysis. We will have six courses by leading experts in geometric analysis, accompanied by several problem sessions and discussion groups.

Speakers and tentative titles:

Please apply for admission to the Summer School on Geometric Analysis by filling out our application form on the website.

### Floer homology and homotopy theory: summer school and conference

Meeting Type: Summer school

Contact: Andrew Blumberg

### Description

These two events will bring together symplectic geometers, low dimensional topologists, and algebraic topologists. The main goal will be to explore the use of homotopy theoretic methods in Floer theory. The summer school (July 10-15) will cover background material, aimed at familiarizing students and researchers with the material in each of the three fields. It will be followed by a research conference (July 17-21).

### Workshop on Infinity-Operads and Applications

Meeting Type: workshop

Contact: Hongyi Chu, Joana Cirici, Oriol Raventós, Markus Spitzweck

### Description

Infinity-operads have attracted a great deal of attention from the homotopy theory community and their potential for applications is now being explored in different fields. This workshop will give its participants the chance to learn about the existing models for infinity operads, the relation between them and some of their most recent applications. The workshop will consist of three mini-courses as well as contributed talks. The participants will be assumed to be familiar with the basic theory of ordinary operads and homotopy theory (that is basic model category theory and basic infinity-category theory).

### Curves of low genus

Meeting Type: conference

Contact: see conference website

### Description

The topics will cover various aspects of the arithmetic and geometry of curves of low genus and their moduli spaces.

### Where Geometry meets Number Theory: a conference in honor of the 60th birthday of Per Salberger

Meeting Type: conference

Contact: see conference website

### Description

### Homotopy Theory: tools and applications

Meeting Type: conference

Contact: Daniel Davis, Mark W. Johnson, Charles Rezk, Vesna Stojanoska

### Description

Preliminary Announcement.

The aim of the conference is to survey recent advances in the fundamental tools of homotopy theory (including abstract homotopy theory, equivariant homotopy, obstruction-theoretic methods), to highlight future directions of research, including applications to chromatic homotopy theory, motivic homotopy theory, and derived algebraic geometry.

Speakers:

Agnes Beaudry, University of Chicago

Mark Behrens, University of Notre Dame

David Blanc, University of Haifa

Anna Marie Bohmann, Vanderbilt University

Hans-Werner Henn, University of Strasbourg

Kathryn Hess, EPFL

Mike Hopkins, Harvard University

Marc Hoyois *, MIT

Rick Jardine, University of Western Ontario

Magdalena Kedziorek, EPFL

Nitu Kitchloo, Johns Hopkins University

Tyler Lawson, University of Minnesota

Jacob Lurie, Harvard University

Haynes Miller, MIT

Jack Morava, Johns Hopkins University

Doug Ravenel, University of Rochester

Birgit Richter, University of Hamburg

Brooke Shipley, University of Illinois at Chicago

Zhouli Xu, University of Chicago

Inna Zakharevich, University of Chicago

*to be confirmed

Others interested in speaking are encouraged to contact the organizers.

Further information will become available at the conference website

http://www.math.illinois.edu/homotopy2017/index.html

and

questions to the conference organizers are welcome at

homotopy2017@math.uiuc.edu

Organizers:

Daniel Davis, University of Louisiana at Lafayette

Mark W. Johnson, Penn State Altoona

Charles Rezk, University of Illinois at Urbana-Champaign

Vesna Stojanoska, University of Illinois at Urbana-Champaign

### Sage Days 87: p-adics+

Meeting Type: software development workshop

Contact: see conference website

### Description

### IHES Summer School: Spectral Properties of Large Random Objects

Meeting Type: conference

Contact: Hugo Duminil-Copin

### Description

The Summer school on "Spectral properties of large random objects" will be held at the Institut des Hautes Etudes Scientifiques (IHES) from July 17 to July 28, 2017. IHES is located in Bures-sur-Yvette, south of Paris (40 minutes by train from Paris).

The school is open to everybody but intended primarily for young participants, including PhD students and postdoctoral fellows.

Studying spectral properties of large random objects has been a very active playground in probability theory, mathematical physics and computer science during the last decades.

The motivations are manifold: viewing random matrices as a model for complicated quantum Hamiltonians, studying random Schrödinger operators to understand the Anderson localization phenomenon, viewing eigenvectors of random matrices as models for eigenmodes of quantized chaotic systems, or understanding the geometry of large (random) graphs such as expanders via the spectral properties of their adjacency matrices. In those studies the emphasis is generally put either on the eigenvalues or the eigenvectors of the object.

The goal of the summer school is to present to the selected students (from master students to postdocs) a panoramic view of this rich area, in order to arouse their interest for some old problems which are coming back on stage, as well as the new exciting horizons of the field.

Some funding is available for young participants (more info at the bottom of the page)

Main courses:

• Charles BORDENAVE (Université de Toulouse) Spectrum of random graphs

• Paul BOURGADE (New York University) Universality and quantum unique ergodicity in random matrix theory

• Frédéric KLOPP (Université Pierre et Marie Curie)

Large systems of interacting quantum particles in a random field

• Eyal LUBETZKY (New York University) Spectral vs. geometric approaches to random walks on random graphs

• Yuval PERES (Microsoft Research) The cutoff phenomenon and rate of escape for Markov chains

• Christophe SABOT (Université de Lyon 1) Self-interacting processes and random Schrödinger operators

• Balint VIRAG (University of Toronto) Operator limits of random matrices

• Simone WARZEL (Technische Universität München)

Topics in random operator theory

Organising Committee:

Nicolas CURIEN (Université Paris-Sud) Hugo DUMINIL-COPIN (IHES) Jean-François LE GALL (Université Paris-Sud) Stéphane NONNENMACHER (Université Paris-Sud)

### Berkovich Spaces, Tropical Geometry and Model Theory

Meeting Type: summer school

Contact: Pablo Cubides Kovacsics

### Description

This summer school aims to gather students and researchers working in the following fields: Berkovich spaces, tropical geometry and model theory. Recent breakthroughs in all three disciplines showed multiple links between them. We are convinced that a fruitful interaction will continue to grow and we consider crucial to encourage and estalish common grounds of communication between researchers.

Pre-courses (2 days) on Berkovich spaces, tropical geometry, model theory.

Courses (3 days):

- Linear series on tropical curves (Matt Baker)
- Berkovich spaces: a different approach by Hrushovski and Loeser (Zoé Chatzidakis)
- Degenerations of complex structures and Berkovich spaces (Mattias Jonsson)

Advanced talks (2 days) by Ducros, Goodrick, Jonsson, Rideau, Rincón, Soto, Turchetti, Welliaveetil

Organizing committee: Alexander Berenstein, Pablo Cubides, Jérôme Poineau.

### Iwasawa 2017

Meeting Type: conference

Contact: see conference website

### Description

This is the seventh Iwasawa conference following conferences in Besancon, Limoges, Irsee, Toronto, Heidelberg, and London.

### Pacific Rim Workshop on Geometric Analysis

Meeting Type: conference

Contact: see conference website

### Description

The conference marks the second joint event of the International Collaborative Research Group (CRG), which includes Australian National University, Beijing International Centre for Mathematical Research, Pacific Institute for the Mathematical Sciences, The University of British Columbia, and University of Washington. It aims to survey the state-of-the-art advances in areas of geometric analysis, differential geometry, and nonlinear partial differential equations. The conference in part celebrates Professor Gang Tian’s 60th birthday.

### Automorphic forms and the Langlands program

Meeting Type: graduate summer school

Contact: see conference website

### Description

The summer school will be an introduction to the more algebraic aspects of the theory of automorphic forms and representations. One of the goals will be to understand the statements of the main conjectures in the Langlands programme. Another will be to gain a good working understanding of the fundamental definitions in the theory, such as principal series representations, the Satake isomorphism, and of course automorphic forms and representations for groups such as GL_n and its inner forms.

### SIAM Conference on Applied Algebraic Geometry

Meeting Type: conference

Contact: see conference website

### Description

### Stacks Project Workshop

Meeting Type: workshop (appropriate for graduate students)

Contact: Pieter Belmans, Aise Johan de Jong, Wei Ho

### Description

This will be a workshop in Algebraic Geometry. The intended participant is a graduate student, or a postdoc, or even a senior researcher. You will work on a single topic in a small group together with a mentor for a week with the aim of producing a text that will be considered for inclusion in the Stacks Project. Part of this process will be seeing how one builds new theory from the foundations. There will also be one or two talks per day covering advanced topics in Algebraic Geometry.

The Stacks project workshop will have some optional activities you won't see at other workshops. Adding references to and finding mistakes in the Stacks project (and fixing them) as well as activities related to LaTeX use, Git, and GitHub. Overall these will be aimed at helping you contribute efficiently to the Stacks Project.

### Students' Conference on Tropical and Non-Archimedean Geometry

Meeting Type: conference

Contact: see conference website

### Description

The follow-up to the 2015 Students' Conference on Tropical and Non-Archimedean Geometry will take place in august 2017 in Regensburg.

Registration will close on May 13th, 2017.

### Topological and Geometric Methods in Quantum Field Theory (NSF-CBMS)

Meeting Type: Workshop, summer school,

Contact: David Ayala, Ryan Grady

### Description

NSF-CBMS conference: "Topological and Geometric Methods in Quantum Field Theory." http://www.math.montana.edu/cbms/ 31 July - 4 August 2017, Bozeman, Montana.

Expert Participants. Dan Freed (principle lecturer) Agnes Beaudry Robert Bryant Sam Gunningham Max Metlitski David Morrison Andy Neitzke

Abstract.
This event will be framed around a series of 10 somewhat self-contained lectures by Dan Freed concerning recent work using stable homotopy theory for predictive results in topological phases of matter. Other key experts will facilitate supplemental discussion sessions with the intent of offering background, context, and examples. The expertise of these participants will represent differential geometry, quantum field theory, and algebraic topology.

This event will be especially designed for graduate students and recent graduates, as well as experienced researchers aiming to enhance their pool of workable knowledge.

Registration. Please register through the event webpage: http://www.math.montana.edu/cbms/ . Deadline for registration is 19 March 2017; there is no registration fee.

There are NSF funds to fully support 30 participants, notably graduate students and recent graduates; these funds will cover food, board, and travel (within the United States). Application for such funding is part of the registration process.

Location. Bozeman, Montana, is an especially splendid place to be through this period of the summer. There are a host of trails near to town, and there is a modest, though active, downtown district.

For any further inquiries please send an email to Ryan Grady: ryan.grady1 at montana.edu .

### Workshop on Algorithms in Number Theory and Arithmetic Geometry

Meeting Type: conference

Contact: Peter Bruin

### Description

The theme of the workshop will be explicit and computational methods in number theory and arithmetic geometry in a broad sense. The format will include scientific talks as well as time for informal collaboration and for coding projects related to (for example) PARI/GP, SageMath or the L-Functions and Modular Forms Database.

### Third Latin American school on Algebraic Geometry and its applications (ELGA 3)

Meeting Type: conference

Contact: Xavier Gómez-Mont, José Seade

### Description

The school is aimed at postgraduate students, postdocs and young researchers.

Introductory courses on research topics in Algebraic Geometry:

Mark de Cataldo: Perverse sheaves and the topology of algebraic varieties.

Duco Van Straten: Differential Forms in Algebraic Geometry and Applications.

Giorgio Ottoviani: Projective Invariants.

Mark Spivakovsky: Introduction to valuation theory and resolution of singularities.

Carolina Araujo: Fano Manifolds.

Lothar Goettsche*: TBA

Financial Assistance:

We will be able to offer some support. Graduate students, junior faculty, women, underrepresented minorities, and persons with disabilities are encouraged to participate and to apply for support. Deadline to request support is March 3th. Early requests will be given preference.

Contact:

elga3@cimat.mx

## August 2017

### Summer School on Trace Methods in Algebraic K-Theory

Meeting Type: summer school

Contact: Benjamin Antieau

### Description

### WIN4: Women in Numbers 4

Meeting Type: workshop

Contact: Jennifer Balakrishnan, Chantal David, Michelle Manes, Bianca Viray

### Description

The focus of the workshop is on supporting new research collaborations within small groups. Before the workshop, each participant will be assigned to a working group according to her research interests. Prior to the conference, the two project leaders will design projects and provide background reading and references for their groups. At the conference, there will be some talks, but there will also be ample time dedicated to working groups. Project leaders will direct their group's research effort and provide mentorship. At the end of the week, members of each research group will describe their group's progress on the research problems as well as future directions for the work.

Applications are now open.

Applications close on January 15, 2017.

### Symplectic geometry - celebrating the work of Simon Donaldson

Meeting Type: conference

Contact: see conference website

### Description

Workshop Theme

A week-long meeting of the world's experts in symplectic geometry and neighbouring fields. We will be celebrating the 60th birthday of Sir Simon Donaldson FRS and his profound influence on the subject. A characteristic of both his work and this meeting will be the influence of (and on) other fields, such as low dimensional topology, algebraic geometry, geometric analysis and theoretical physics. This is a joint INI - CMI workshop.

Speakers to include:

```
Mina Aganagic (Berkeley)
Sir Michael Atiyah (Edinburgh)
Denis Auroux (Berkeley)
Kenji Fukaya (Stony Brook)
Mikhail Gromov (IHES, Paris)
Nigel Hitchin (Oxford)
Eleny Ionel (Stanford)
Frances Kirwan (Oxford)
Peter Kronheimer (Harvard)
Dusa McDuff (Barnard)
Emmy Murphy (MIT)
Tom Mrowka (MIT)
Peter Ozsváth (Princeton)
Zoltán Szabó (Princeton)
Paul Seidel (MIT)
Ivan Smith (Cambridge)
Song Sun (Stony Brook)
Clifford Taubes (Harvard)
Thomas Walpuski (MIT)
Katrin Wehrheim (Berkeley)
```

### Topology Ecuador 2017

Meeting Type: conference

Contact: Daniela Egas, Andrea Moreira, John Skukalek, Marc Stephan

### Description

This conference will cover a wide range of topics from algebraic topology to non-commutative geometry. Its purpose is to contribute to the development of these fields in Ecuador and to provide a meeting point for Latin-American mathematicians with other experts from around the world.

### Homotopy Theory in the Ecliptic: Chromatic, Equivariant, and Motivic Mathematics

Meeting Type: conference

Contact: Agnes Beaudry, Irina Bobkova, Safia Chettih, Mike Hill, John Lind, Kyle Ormsby, Angelica Osorno

### Description

### Minischool on "G2 manifolds"

Meeting Type: Minischool

Contact: Spiro Karigiannis

### Description

This two-day minischool will serve to prepare graduate students, postdoctoral fellows, and other researchers less familiar with G2 manifolds for the five-day workshop on G2 manifolds immediately following, on Aug 21-25. Tentative mini-course topics include:

Registration available now on the minischool website.

### Algebraic K-theory and Arithmetic

Meeting Type: conference

Contact: Grzegorz Banaszak, Piotr Krasoń, Wiesława Niziol

### Description

Algebraic K-theory and arithmetic is the second conference in this series at Polish Academy of Sciences Conference Center in Będlewo. The first conference was in 2012.

Main Topics: Algebraic K-theory and Number Theory, Algebraic cycles and Algebraic K-theory, Motives and Motivic Cohomology, Algebraic K-theory and Arithmetic Geometry.

### Low-dimensional Topology and Number Theory

Meeting Type: invitational conference

Contact: see conference website

### Description

Organisers

Paul E. Gunnells, Amherst

Walter D. Neumann, New York

Adam S. Sikora, New York

Don B. Zagier, Bonn

### Interactions between Representation Theory and Algebraic Geometry

Meeting Type: conference

Contact: see conference website

### Description

### Maryland Analysis and Geometry Atelier

Meeting Type: conference and summer school

Contact: Paolo Piccione, Yanir A. Rubinstein, Richard A. Wentworth

### Description

The Maryland Analysis and Geometry Atelier aims to bring together students and researchers working on analytic aspects of problems in geometry and dynamics.

The program will include a mix of mini-courses and research talks with an emphasis on introducing a variety of geometric and analytic techniques that could have wide applications to different problems in geometric analysis and related areas.

The main events of the workshop will be three 5-hour minicourses . In addition, each day there will be one research talk. The intention is to also allow ample time for discussion and collaboration.

Financial support for this event is available by a UMD (University of Maryland)-FAPESP (Fundacao de Amparo a Pesquisa do Estad de Sao Paulo) seed grant to Piccione and Rubinstein and by the National Science Foundation GEAR (GEometric structures And Representation varieties) network.

Graduate students, postdocs, and early-career mathematicians are especially encouraged to participate and apply for financial support.

The registration deadline for the Maryland Analysis and Geometry Atelier is April 15th.

### Workshop on "G2 manifolds"

Meeting Type: Workshop

Contact: Spiro Karigiannis

### Description

A central theme in differential geometry is the existence and classification of “optimal geometric” structures. An important class of optimal metrics in Riemannian geometry are the Einstein metrics, especially metrics with special holonomy. These include in particular the Calabi-Yau and more generally the Kaehler-Einstein metrics, the study of which is by now a classical area of research at the intersection of geometric analysis and algebraic geometry. More recently, there has been increasing interest in G2 manifolds and other Riemannian manifolds with special geometric structures (such as Spin(7) manifolds or nearly Kaehler manifolds) whose study are not amenable to classical tools of algebraic geometry. This is partly due to the fact that all of these manifolds play important roles as ingredients for compactifications in string theory and M-theory. The area began to really develop in the 1980’s and 1990’s with the pioneering work of Bryant, Salamon, Joyce, Kovalev, Hitchin, and others. It is now one of the most exciting new frontiers in geometric analysis. Some of the key objectives include constructing new complete and compact examples (both by elliptic glueing methods and by parabolic flow techniques); finding topological invariants and obstructions to existence; and understanding the local and global structure of the moduli spaces of such structures.

Principal Speakers:

* to be confirmed

Registration available now on the workshop website.

### Dyson-Schwinger equations, topological expansions, and random matrices

Meeting Type: conference

Contact: Ivan Corwin

### Description

Understanding the large dimension asymptotics of random matrices or related models such as random tilings has been a hot topic for the last twenty years within probability, mathematical physics, and statistical mechanics. Because such models are highly correlated, classical methods based on independent variables fail. Special cases have been studied in detail thanks to specific forms of the laws, such as determinantal laws. These lectures will investigate a general class of models using the so called Dyson-Schwinger equations or generalizations such as Nekrasov's equations. The idea is similar to Stein's method in that the observables are approximate solutions of equations that can be solved asymptotically.

Alice Guionnet (Lyon) will give ten main lectures, divided into two per day. Besides these lectures there will be supplementary lectures by other senior researchers attending the school, including:

Charles Bordenave (Toulouse)

Gaetan Borot (Bonn)

Paul Bourgade (NYU)

Vadim Gorin (MIT)

Sylvia Serfaty (NYU)

This school is intended for graduate students and postdocs who are starting to learn random matrix theory and have some background in probability. Lecture notes will be distributed in advance for preparation and tutorials and problem sessions will be run throughout the school.

### Motives for periods

Meeting Type: summer school

Contact: see conference website

### Description

Periods are a class of complex numbers obtained by integrating algebraic differential forms over algebraically-defined domains. From the modern point of view, they appear as coefficients of the comparison isomorphism between de Rham and Betti cohomology of varieties over number fields. This is how motives enter the game.

The aim of this summer school is to introduce students to the applications of different categories of motives to concrete questions on periods. The possibility of giving non-conjectural constructions of the motivic Galois group has opened the way to major new results: a proof of Hoffman's conjecture on multiple zeta values by Brown, and a proof of a geometric analogue of the Kontsevich-Zagier conjecture by Ayoub.

### Curves and L-functions

Meeting Type: summer school, conference

Contact: see conference website

### Description

Week 1: PhD Summer school "Curves, L-functions, and Galois Representations" Four lecture courses (mornings) and projects/exercise sessions (afternoons)

- Galois representations by Tim and Vladimir Dokchitser
- L-functions and BSD by Adam Morgan
- Selmer groups and descent by Michael Stoll
- Modularity by Jack Thorne

Week 2: Workshop "Arithmetic of Hyperelliptic Curves"

## September 2017

### Locally Symmetric Spaces: Analytical and Topological Aspects

Meeting Type: long-term research program

Contact: see conference website

### Description

During the 2017-18 academic year, the School will have a special program on Locally Symmetric Spaces: Analytical and Topological Aspects. Akshay Venkatesh of Stanford University will be the Distinguished Visiting Professor.

The topology of locally symmetric spaces interacts richly with number theory via the theory of automorphic forms (Langlands program). Many new phenomena seem to appear in the non-Hermitian case (e.g., torsion cohomology classes, relations with mixed motives and algebraic K-theory, derived nature of deformation rings). One focus of the program will be to try to better understand some of these phenomena.

Much of our understanding of this topology comes through analysis ("Hodge theory"). Indeed harmonic analysis on locally symmetric spaces plays a foundational role in the theory of automorphic forms and is of increasing importance in analytic number theory. A great success of such harmonic analysis is the Arthur-Selberg trace formula; on the other hand, the analytic aspects of the trace formula are not fully developed, and variants such as the relative trace formula are not as well understood. Thus analysis on such spaces, interpreted broadly, will be another focus of the program.

### Automorphic Forms and Arithmetic

Meeting Type: invitational conference

Contact: see conference website

### Description

```
Organisers
```

Valentin Blomer, Göttingen

Emmanuel Kowalski, Zürich

Philippe Michel, Lausanne

### Rationality, stable rationality and birationally rigidity of complex algebraic varieties

Meeting Type: Summer School

Contact: Ugo Bruzzo, Pietro De Poi, Francesco Zucconi

### Description

The aim of the school is to bring together 20/30 young researchers in a cosy contest to teach them new results and methods on the generalised rationality problems, e.g. stable rationality, and the birational rigidity problem for rationally connected varieties.

The two main courses will also be enriched by series of complementary lectures mainly focused on explicit calculations taught by two assistants who are distinguished researches themselves.

LECTURERS:

Claire Voisin (Collège de France) Course Title: Stable birational invariants and the generalised Lüroth problem Supporting lecturer: Mingmin Shen (University of Amsterdam)

Ivan Cheltsov (University of Edinburgh) Course Title: Birationally rigid and nearly birationally rigid varieties Supporting lecturer: Hamid Ahmadinezhad (Loughborough University)

To be admitted, for bureaucratic reasons, it is compulsory to pay a participation fee some days before the starting of the school. This fee includes half board for 6 days, and it will be refunded upon request.

Deadline for full reimbursement of the fee: 31st May, 2017.

We can refund partially travel and other expenses for a limited number of participants. Deadline for this request: 31st May, 2017.

### International Conference on Class Groups of Number Fields and Related Topics

Meeting Type: conference

Contact: see conference website

### Description

lass groups of number fields and their cardinalities (i.e, class numbers) have been well studied since the time of Gauss. The study of class groups of number fields became the heart of algebraic number theory after the efforts of Kummer (towards FLT), Dedekind, Kronecker etc. In spite of long history of active research, class groups and their cardinalities remain one of the most mysterious object in algebraic number theory with exceptions like 'finiteness of imaginary quadratic fields with class number one'.

There are two directions which are actively being explored in last 50 years or so. One being the study of annihilators of class groups (results of Iwasawa and Sinnot being corner stone), and, the other being Cohen-Lenstra heuristics. Annihilators of class groups give vital informations about class numbers (e.g. Theorems of Iwasawa and Sinnot) and P. Mihailescu used them very cleverly to solve the longstanding conjecture of Catalan. Though, we are far from proving Cohen-Lenstra heuristics but there has been many small steps in this direction in last 50 years. Infinitude of family of number fields of a given degree with class number divisible by a given number has been established by many mathematicians. Moreover some significant results have been obtained due to efforts of a few mathematicians on the density of quadratic number fields with class number a multiple of a given integer.

Another aspect which we shall highlight during the conference is the computation of class numbers of cyclotomic fields. Computing class number of cyclotomic fields is extremely tedious and we have such computations available only for cyclotomic fields of prime conductor less than 70 (and up to 163 under GRH). In an article, R. Schoof considers a subgroup of class group of maximal real subfield of p-th cyclotomic field whose cardinality can be computed easily. Schoof speculates that, most likely, this subgroup equals the class group of maximal real subfield. If the speculation of Schoof is proven right then it will make computation of class number of cyclotomic fields very easy.

The aim of this conference is to bring various experts on the subject at one place and provide young number theorists of the country a very needed thrust (it is after long time this topic is being highlighted so exclusively, even worldwide). Also we hope that this will kindle interest of upcoming generation in Algebraic Number Theory.

### VBAC2017: Motivic Methods and Derived Categories

Meeting Type: conference

Contact: see conference website

### Description

VBAC2017 (Vector Bundles on Algebraic Curves 2017) Motivic Methods and Derived Categories

Sponsors: DFG Priority Programme 1786: Homotopy Theory and Algebraic Geometry SFB/TR45: Periods, moduli spaces and arithmetic of algebraic varieties

Organisers: Georg Hein, Marc Levine

Minicourses: Emanuele Macri: Bridgeland Stability Goncalo Tabuada: Noncommutative Motives

Invited speakers: Aravind Asok, Marcello Bernardara, Jean Fasel, Daniel Halpern-Leistner, Jesse Kass, Markus Reineke, Wolfgang Soergel, David Stapleton* (*=to be confirmed).

Circulated on behalf of the VBAC Committee: Peter Newstead (Chair), Usha Bhosle, Steven Bradlow, Leticia Brambila-Paz, Ugo Bruzzo, Carlos Florentino, Oscar Garcia-Prada, Peter Gothen, Daniel Hernandez Ruiperez, Alastair King, Herbert Lange, Antony Maciocia, Ignasi Mundet i Riera, Christian Pauly, Alexander Schmitt, Andras Szenes.

### British Algebraic Geometry meeting (BrAG)

Meeting Type: conference

Contact: Julius Ross

### Description

BrAG will become a series of regular meetings of British algebraic geometers. Our goal is to create a series that further strengthens the British algebraic geometry community, and that integrates PG students and young researchers. The meetings will feature a number of pre-talks for graduate students, a poster session, and will include plenty of time for informal interactions between the participants.

### Diophantine Problems (DIOP)

Meeting Type: conference

Contact: Daniel Loughran

### Description

### Joint ÖMG-DMV meeting

Meeting Type: conference

Contact: Prof. Clemens Fuchs (chair of the organizing committee)

### Description

The board of the Austrian Mathematical Society (ÖMG) and the organizing committee cordially invite to the 19th International Congress of the ÖMG from September 11-15, 2017 in Salzburg. This conference is also the Annual Meeting of the Deutsche Mathematiker-Vereinigung (DMV).

The scientific program consists of:

9 plenary lectures by: Michael Eichmair (Vienna), Lawrence Craig Evans (Berkeley), Ursula Hamenstädt (Bonn; Emmy-Noether-Lecture), Martin Hairer (Warwick), Gabriele Nebe (Aachen), Carola Schönlieb (Cambridge), Gigliola Staffilani (MIT), Michael Zieve (Michigan), Aleksey Kostenko (Vienna);

contributed talks organized in 17 sections;

8 minisymposia;

a public lecture (which will be given by Walter Schachermayer).

### Periods and Ricci flat manifolds

Meeting Type: workshop

Contact: see conference website

### Description

Invited speakers: Arnaud Beauville (Nice), Gilberto Bini (Milano), Michele Bolognesi (Montpellier), Christian Böhning (Warwick), Yohan Brunebarbe (Uni Zürich), Chiara Camere (Milano), Martin Gulbrandsen (Stavanger), Martí Lahoz (Paris 7), Adrian Langer (Warsaw), Laurent Manivel (Marseille), John Christian Ottem (Oslo) - tbc, Victor Przyjalkowski (Moscow), Ulrike Riess (ETH Zürich), Gregory Sankaran (Bath), Alessandro Verra (Roma Tre)

### Instruments of Algebraic Geometry

Meeting Type: summer school, conference

Contact: see conference website

### Description

A summer school and workshop will take place in Bucharest in September 2017. Their goal is to cover some active topics in algebraic geometry: homological methods, discrete and arithmetic aspects, and singularities. Besides the mathematics, a special feature of this event will be a close relation to the George Enescu Music Festival, which takes place in Bucharest every other year. Moreover, an IMAGINARY exhibition will be presented during the three weeks of the festival, and further events involving a direct interaction of mathematics and music - and of mathematicians and musicians - are planned.

Limited financial support for participants will be available. Priority will be given to Ph.D. students and early career researchers with excellent scientific recommendations and exceptional promise. The application deadline for financial support is 1st June 2017.

Topics:

Homological methods Syzygies of a projective variety are very fine numerical invariants that control the embedding of the variety. From the syzygies, one can easily recover the Hilbert function, however, their outmost importance comes from the fact that they carry intrinsic geometric properties. They can be used to extract information on the geometry of moduli spaces of polarized varieties.

Discrete aspects They originate in the theory of toric varieties linking algebraic varieties to convex geometry and combinatorics. Nowadays, the field has expanded into several directions like tropical geometry, Berkovich-spaces, and Newton-Okounkov bodies. Algebro-geometric theories like the minimal model program have counterparts in discrete geometry.

Singularities Singularity theory is essential in the classification of algebraic varieties. While the classification in dimension one and two can be done in the smooth setting, from dimension three on the minimal model program heavily relies on singular varieties. Moreover, they play an interesting role in mirror symmetry where resolutions and deformations are interchanged.

Arithmetic geometry With Peter Scholze being one of the speakers for a series of four lectures, we shall focus on perfectoid spaces, and integral de Rham theory. With Yves André being one of the lecturers, we shall have some emphasis on motivic theory over fields, and periods. In addition, we expect some activity around the study of rational points and the index of specific varieties over p-adic fields and number fields. This should be covered by Olivier Wittenberg and other mathematicians around him.

### Second Japanese-European Symposium on Symplectic Varieties and Moduli spaces

Meeting Type: conference

Contact: see conference website

### Description

### Modern Moduli Theory graduate school

Meeting Type: summer school

Contact: Dominic Joyce, Kevin McGerty, Balazs Szendroi

### Description

The Graduate School will consist of lecture series and individual lectures on certain aspects of algebraic geometry and geometric representation theory. Themes within algebraic geometry will include moduli spaces of sheaves on Calabi-Yau manifolds, and more generally moduli spaces of objects in Calabi-Yau categories, especially their derived structures in shifted symplectic geometry and shifted Poisson geometry, following Calaque-Pantev-Toën-Vaquié-Vezzosi. A related set of lectures will discuss different flavours of Donaldson-Thomas invariants including the cohomological Hall algebra approach of Kontsevich-Soibelman. The geometric representation theory strand will focus on Hall algebras and higher Hall algebras, modern analogues of Beilinson-Bernstein localisation, as well as aspects of quantization.

### Workshop: Non-Positively Curved Groups and Spaces

Meeting Type: workshop

Contact: Alexander Engel

### Description

There will be 3 mini-courses (each 3 lectures 75 min. long) and around 9 invited and contributed talks. Deadline for applications for contributed talks is May 15th, 2017.

### Modern Moduli Theory Clay workshop

Meeting Type: conference

Contact: Dominic Joyce, Kevin McGerty, Balazs Szendroi

### Description

The workshop will focus on modern approaches to moduli problems in algebraic geometry, including derived structures on moduli spaces such as shifted symplectic and shifted Poisson structures, novel quotient constructions, and relationships to geometric representation theory.

### Open Source Computation and Algebraic Surfaces

Meeting Type: conference

Contact: see conference website

### Description

We propose a workshop focused on designing and implementing open-source code for studying the geometry and arithmetic of surfaces. We will emphasize the development of practical skills for computer experimentation. We have two key objectives: to implement cutting-edge algorithms for counting points and computing zeta functions for surfaces, and to develop functionality for manipulating indefinite lattices.

K3 surfaces form a natural testing ground for arithmetic and geometric conjectures. These surfaces bridge a dimensional gap: they may be viewed as higher-dimensional analogues of elliptic curves, whose arithmetic finds applications in number theory and cryptography, or as lower-dimensional versions of Calabi-Yau manifolds or holomorphic symplectic varieties. Historically, arithmetic geometry has focused on understanding the properties of curves. The recent development of algorithms for, e.g., zeta-function computations, provide an opportunity to make significant advances in computational understanding of surfaces.

A robust open-source software infrastructure is of central importance for testing and reproducing mathematical experiments. Without the ability to inspect and modify code, computational exploration is opaque. SageMath offers a widely used, accessible platform for creating and sharing research mathematical software.

Objectives. Our first objective is to incorporate new algorithms for counting points and computing zeta functions of K3 surfaces in SageMath. These algorithms allow us to test conjectures in arithmetic and explore the number-theoretic implications of mirror symmetry. Historically, the theoretical and computational framework for studying zeta functions of surfaces and higher-dimensional varieties has been very limited. This situation has changed in recent years, with pioneering work including that of van Luijk in [14], Elsenhans and Jahnel in [7] and Costa and Tschinkel in [5]. Meanwhile, theoretical descriptions of the way zeta functions for projective Calabi-Yau hypersurfaces vary under one-parameter deformations have been developed (cf. [8], [12], [15]). These developments have sparked renewed interest in the arithmetic implications of mirror symmetry for K3 surfaces and Calabi-Yau varieties more generally, as seen in [1] and [9]. Making code for computing zeta functions widely available will spur the development of new methods for analyzing the arithmetic of surfaces.

In computer algebra systems, methods for working with positive definite lattices are widely available. However, functionality for indefinite lattices is essentially non-existent. The second major objective of this workshop is to bridge this gap.

Indefinite integral lattices are omnipresent in algebraic geometry. The cup product on an algebraic surface equips its middle integral cohomology group (and thus its Neron-Severi group) with the structure of an indefinite lattice. In recent years, holomorphic symplectic manifolds have become a burgeoning area of research. Via the Bogomolov-Beauville-Fujiki quadratic form, we may give their second cohomology group a lattice structure as well.

Consider, in particular, a complex K3 surface. Its second integral, singular cohomology group is a lattice of signature (3,19) which admits a weight two Hodge structure (corresponding to a complex line of the complexified lattice). The Torelli Theorem for K3 surfaces states that this datum determines the surface up to isomorphism. Over the years, many people have employed the following strategy: pick an important geometric property of a K3 surface, reformulate the property in terms of lattices and Hodge structures, and apply the powerful techniques of lattice theory to prove a theorem. This strategy has been tremendously successful in the study of automorphisms and their fixed point sets, Brauer groups, holomorphic dynamics, moduli, elliptic fibrations and their Mordell-Weil lattices, and more recently in exploration of the Umbral Moonshine phenomenon.

Recently there has been some success in combining theoretical lattice-analysis techniques with computer aided calculations. See e.g. [2, 3, 4, 6, 10, 11, 13]. In each of these projects, the authors programmed their own implementation of the calculus of indefinite lattices. Having a reliable toolbox at hand would open the field to new participants and avoid constant re-invention of the wheel. Future applications of these techniques include generalizations to the holomorphic symplectic setting, where a Torelli theorem is now available, deepening connections to Umbral Moonshine and identifying missing automorphisms, and linking to the positive-characteristic setting and exploring the phenomenon wherein Picard ranks jump in a family of surfaces.

Western Canada in general and BIRS in particular is a natural center for advances in arithmetic geometry. Our workshop extends existing networks, building on the success of the Women in Numbers and Alberta Number Theory Days series. Simultaneously, our emphasis on developing concrete computational skills provides an excellent framework for engaging junior scholars and building research connections.

## October 2017

### p-adic Cohomology and Arithmetic Applications

Meeting Type: conference

Contact: Tomoyuki Abe, Chris Lazda, Kiran Kedlaya, Ambrus Pal

### Description

These exciting new trends emerging in the field are of course deeply interwoven, as we already mentioned, and by hosting this workshop we hope to encourage new progress in these areas by promoting both predictable and unpredictable synergies between them. For example, extending the scope of p-adic cohomology will require a more sophisticated view of the foundations of the subject in order to cope with these more general situations, and will in turn feed into many of the other areas of interest, in particular representation theory and the local Langlands correspondence by providing a more powerful language in which to discuss these questions. It is important to note that p

-adic cohomology is often characterised by a plethora of different approaches to the subject, each of which has its own particular perspective and scope of application. By drawing together people working on all aspects of the theory, and building on the successful conference hosted by 2 of the organisers at Imperial College London in March 2015, we will provide a platform for a cross-fertilisation of the raft of new ideas in all these different approaches, and stimulate new developments across the whole breadth of the subject. Here we list a few topics and the expected interactions which we hope to foster via the workshop.

Foundations and theory over non-perfect fields} Traditionally, p -adic cohomology theories have been expressed for varieties over perfect ground fields of characteristic p . While much of the theory still works over non-perfect fields, arithmetic considerations (in particular the general phenomenon of semistable reduction, as well as analogies with the ℓ -adic theory) lead one to expect certain refinements of existing p -adic cohomologies (such as rigid cohomology) when working over such non-perfect fields. As a first step in this direction, the basics of this picture have been recently worked out over the simplest of non-perfect fields, namely Laurent series field in one variable, which has paved the way for a whole host of applications, such as a p -adic version of the weight monodromy conjecture and good reduction criteria for curves. This approach appears to be a rich source of new arithmetic results on varieties in characteristic p , although there is still much more foundational work to be done, both in the case of Laurent series fields and in terms of moving towards other examples such as global fields or higher dimensional local fields. On there other hand the groundbreaking work of Caro in the last decade has culminated in the proof of the existence of a 6 operations formalism in p -adic cohomology, including a full theory of weights \cite{padicwt . We expect to see interactions between these two strides of research, and the workshop will provide the perfect environment to achieve this.

The Langlands program and links with representation theory} One of the importance of the original theory of algebraic D -modules, which is over a field of characteristic zero, is that it has various application to representation theory. Beilinson--Bernstein correspondence is one of the most famous such examples. About 20 years ago Berthelot proposed a framework to establish a 6 functor formalism for schemes over fields of positive characteristics by pursuing an analogy with algebraic D -modules, and named it arithmetic D -module theory. With the above mentioned work of Caro, the foundations of the theory are essentially in place, and attention is turning to a new stage. As in the classical situation, it is hoped that the theory will prove a powerful tool for representation theory, including the p -adic Langlands program. A similar such application of D -module theory over rigid analytic spaces over p -adic fields has been already found by Ardakov--Wadsley \cite{ardwad , who used their theory to answer some representation theoretical problems which arose in the new p-adic local Langlands program.

There is a closely related work of Huyghe, Patel, Schmidt and Strauch on localisation theorems in the setting of arithmetic D -modules of Berthelot (see [HPSS}) which proves that there is an equivalence of categories between the category of locally analytic admissible representations of some split reductive group over a finite extension of Qp, and the category of coadmissible arithmetic D-modules over the rigid analytic space attached to the flag variety of the group. Similarly, the 6 operations formalism has been used by Abe \cite{abelang} to prove a p-adic Langlands correspondence in the function field setting, and thus prove Deligne's ``petits camarades cristallins" conjecture on the existence of p-adic companions to compatible systems of ℓ-adic Galois representations (at least over curves). Finally let us mention the work of Christian Johannsson, who studied the classicality for small slope overconvergent automorphic forms on certain higher dimensional Shimura varieties (see \cite{Jo]), a work whose primary innovation is to use a robust formalism of p-adic cohomology. These works all represent different aspects of the p-adic Langlands program, both over number fields and function fields, and all rely heavily on the methods of p-adic cohomology. Promoting co-operation between the experts of this subject and the leaders of the foundational theory of p

-adic cohomology will therefore be essential in progressing this exciting new direction of research.

The de Rham--Witt complex and Iwasawa theory} One of the original motivations of Grothendieck and Berthelot for inventing crystalline cohomology as a p -adic companion to the family of ℓ -adic cohomologies produced by the \'{e}tale theory was to explain p -torsion phenomenon. While integral crystalline cohomology achieves this for smooth and proper varieties, the extension to a `good' cohomology theory for arbitrary varieties, which reached its zenith in the proof of the 6 operations formalism by Caro, has been achieved only for rational coefficients, i.e. after tensoring with Q . This therefore still leaves open the question of what an integral p -adic theory should look like for open or singular varieties, which has been the subject of much recent work in the field, in particular the study of the overconvergent de Rham--Witt complex by Davis, Langer and Zink \cite{dlz . This now seems to provide a good candidate for smooth (but possibly open) varieties, although there are still many important open questions still to answer, including comparisons with other candidates such as integral Monsky--Washnitzer cohomology.

This is very closely related to the study of p -adic properties of L-functions in characteristic p where most of the work recently has been done on 1-dimensional families of abelian varieties, for example [KT}, \cite{Pa} and \cite{TV} which look at the refined Birch--Swinnerton-Dyer conjecture, the integrality of p-adic L-functions and the equivariant Tamagawa number conjecture, respectively. What is common in these works is the crucial use of integral p

-adic cohomology theories predating the construction in \cite{dlz], typically log crystalline cohomology. Therefore they are forced either to reduce the general case to the semi-stable one, or worse, restrict to the situation when the abelian scheme is semi-stable and the considered Galois covers of the base are tame. This demonstrate the limitations of these methods, but with sufficient progress on the finiteness properties of the the overconvergent de Rham--Witt complex we expect that this area would start to develop very rapidly.

Relations with function field arithmetic} We already mentioned the deep analogy and the cross-fertilisation which occurred between p -adic Hodge theory and its function field analogue at a crucial point of their development. However there are other areas of p -adic cohomology and function field arithmetic which are closely analogous and more intimate interaction would benefit both. For example a central object of study in function field arithmetic is Goss L -functions of function field motives (see for example [T1]). These motives have a cohomological theory with a trace formula (see \cite{BP1 ), but the theory does not admit 6 operations. It would greatly benefit the topic if the methods of p-adic cohomology were successfully transported into it. On there hand the transcendence theory of special values of Goss L-functions is highly developed, but uses cohomological, Tannakian and analytic methods which would be very familiar to experts of p-adic cohomology (such as Dwork's trick) if they knew them. We hope that workshop could bring the birth of a brand new transcendence theory of p-adic periods in characteristic p.

Other topics Let us mention a few more topics which were intensively studied recently and which all have deep connections to the main topic of the proposed workshop, but which we could not describe in much detail for the lack of space: p-adic differential equations, crystalline fundamental groups and p-adic Simpson correspondence, p-adic Hodge theory and p-adic representations. We just remark in passing that p-adic differential equations play a fundamental role in the foundations of the theory, the study of crystalline fundamental groups is necessary for removing some of the thorny problems encountered in the Langlands program over function fields, and some form of a p-adic Simpson correspondence might be the way to overcome these, while p-adic Hodge theory remains perhaps the single most important application of p-adic cohomology via the theory of p-adic representations. So we expect that they will remain in the focus of research, and by inviting experts in these fields we will not only spread knowledge of some of the powerful new methods available in p-adic cohomology, but also to inspire those working in the field with potential new applications of their research.

Bibliography

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[1] abelang T.~Abe, Langlands correspondence for isocrystals and existence of crystalline companion for curves, arXiv:1310.0528, (2013).
[2] padicwt T.~Abe and D.~Caro, Theory of weights in {p
```

}-adic cohomology, arXiv:1303.0662v3, (2014).

[3] ardwad K.~Ardakov and S.~Wadsley, On irreducible representations of compact {p }-adic analytic groups, Ann. of Math., 178 (2013), 453--557.

[4] Ba1 F. Baldassarri, Continuity of the radius of convergence of differential equations on p -adic analytic curves, Invent. Math. 182 (2010), 513--584.

[5] cohcrist P.~Berthelot, Cohomologie cristalline des sch{\'e}mas de characteristic {p>0 }, Lecture Notes in Mathematics 407, Springer-Verlag, Berlin-New York, 1974.

[6] B1 P.~Berthelot, Finitude et puret\'e cohomologique en cohomologie rigide, Invent. Math. 128 (1997), 329--377.

[7]{Bess1} A.~Besser, A generalization of Coleman's p -adic integration theory, Invent. Math. 142 (2000), 397--434. \bibitem[8] Bess2 A.~Besser, Coleman integration using the Tannakian formalism, Math. Ann. 322 (2002), 19--48.

[9] BP1 G.~B\"ockle and R.~Pink, Cohomological theory of crystals over function fields, Tracts in Mathematics 5, European Mathematical Society, (2009).

[10] dlz C.~Davis, A.~Langer, and T.~Zink, Overconvergent de {R}ham-{W}itt cohomology, Ann. Sci. \'Ec. Norm. Sup\'er. 44 (2011), 197--262.

[11] DW B.~Dwork, On the rationality of the zeta function of an algebraic variety, Amer. J. Math. 82 (1960), 631--648.

[12] G1 M.~Gros, R\'egulateurs syntomiques et valeurs de fonctions L p -adiques I, with an appendix by Masato Kurihara, Invent. Math. 99 (1990), 293--320.

[13] G2 M.~Gros, R\'egulateurs syntomiques et valeurs de fonctions L p -adiques II, Invent. Math. 115 (1994), 61--79.

[14] grothcrys A.~Grothendieck, Crystals and the de {R}ham cohomology of schemes}, in {\it Dix {e}xpos\'es sur la {c}ohomologie des {s}ch\'emas, North-Holland, Amsterdam--Paris, 1968, pp. 306--358.

[15] Ha U.~Hartl, Period spaces for Hodge structures in equal characteristic, Ann. of Math. 173 (2011), 1241--1358.

[16] HPSS C.~Huyghe, D.~Patel, T.~Schmidt, and M.~Strauch, D† -affinity of formal models of flag varieties, arXiv:1501.05837, (2015).

[17] hyodokato O.~Hyodo and K.~Kato, Semi-stable reduction and crystalline cohomology with logarithmic poles, Ast\'erisque 223, 1994, pp. 221--268.

[18] Jo C.~Johannsson, Classicality for small slope overconvergent automorphic forms on some compact PEL Shimura varieties of type C, Math. Ann. 357 (2013), 51--88.

[19] KT K.~Kato and F.~Trihan, On the conjectures of Birch and Swinnerton-Dyer in characteristic p>0, Invent. Math. 153 (2003), 537--592.

[20] kedzeta K.~Kedlaya, Computing zeta functions via {p }-adic cohomology}, in {\it Algorithmic number theory, Lecture Notes in Comput. Sci. 3076, Springer-Verlag, Berlin-New York, 2004, pp. 1--17.

[21] Ke1 K.~Kedlaya, Convergence polygons for connections on nonarchimedean curves, arXiv:1505.01890v2, to appear in the proceedings of the Simons Symposium on non-archimedean and tropical geometry, (2015).

[22] KL K.~Kedlaya and R.~Liu, Relative p-adic Hodge theory: foundations, Ast\'erisque, to appear, 210 pages.

[23] kim1 M.~Kim, The unipotent Albanese map and Selmer varieties for curves, Publ. RIMS, Kyoto Univ. 45 (2009), 89--133.

[24] lauderzeta A.~Lauder, A recursive method for computing zeta functions of varieties, LMS J. Comput. Math. 9 (2006), 222--269.

[25] LP C.~Lazda and A.~P\'al, Rigid cohomology over Laurent series fields, Algebra and Applications, Springer--Verlag, London, to appear, 191 pages.

[26] messing W.~Messing, The crystals associated to {B}arsotti-{T}ate groups: with applications to abelian schemes, Lecture Notes in Mathematics 264, Springer-Verlag, Berlin-New York, 1972.

[27] MW P.~Monsky and G.~Washnitzer, Formal cohomology. I, Ann. of Math. 88 (1968), 181--217.

[28] Mo M.~Morrow, A Variational Tate conjecture in crystalline cohomology, preprint, (2015).

[29] Pa A.~P\'al, The Manin constant of elliptic curves over function fields, Algebra Number Theory 4 (2010), 509--545.

[30] PP J. Poineau and A. Pulita, The convergence Newton polygon of a p-adic differential equation IV: local and global index theorems, arXiv:1309.3940v1 (2013).

[31] T1 L. Taelman, Special L-values of Drinfeld modules, Ann. of Math. 175 (2012), 369--391.

\bibitem[32]{TV} F.~Trihan and D.~Vauclair, A comparison theorem for semi-abelian schemes over a smooth curve, arXiv:1505.02942, (2015).

### Workshop on motivic and equivariant homotopy theory

Meeting Type: workshop

Contact: Martin Frankland, Manh Toan Nguyen, Konrad Voelkel

### Description

See the website.

### Topics in arithmetic and algebraic geometry

Meeting Type: autumn school

Contact: Dino Festi, Ariyan Javanpeykar, Davide Cesare Veniani

### Description

This is an Autumn School of the SFB/TRR 45 Bonn-Essen-Mainz financed by the DFG (Deutsche Forschungsgemeinschaft).

This school is intended for advanced master students, PhD students, and young researchers in algebra, number theory and geometry.

### Lie Theory, Geometry, and Differential Equations

Meeting Type: Fall School

Contact: Ilka Agricola (on behalf of all organizers)

### Description

This joint Fall School of the Math Departments of Marburg and Gießen takes places at Castle Rauischholzhausen near Marburg, a university owned conference center known for its casual atmosphere.

We invite students and young scientists working in Lie theory and adjacent areas from analysis, algebraic geometry, and differential geometry to participate!

There will be four series of lectures:

Hansjörg Geiges (Köln) -- Contact geometry and dynamics

Nicolas Perrin (Versailles, France) -- Varieties with a group action

Mihaela Pilca (Regensburg) -- Locally conformally Kähler geometry

Anke Pohl (Jena) -- Eigenfunctions on locally symmetric spaces

Furthermore, there will a selection of talks by participants and a poster session. All talks of the Fall School will be in English.

### Western Algebraic Geometry Symposium

Meeting Type: conference

Contact: see conference website

### Description

WAGS is a twice-yearly meeting of algebraic geometers in the western half of the United States and Canada that traces its origins back to the Utah-UCLA Algebraic Geometry Seminar started in 1989.

### Constructing cryptographic multilinear maps

Meeting Type: workshop

Contact: see conference website

### Description

This workshop, sponsored by AIM, the Alfred P. Sloan Foundation, and the NSF, will be devoted to the problem of constructing secure and efficient cryptographic multilinear maps. Cryptographic multilinear maps are a powerful tool in cryptography. They solve many long-standing open problems in cryptography and computer security that currently cannot be solved any other way. Unfortunately, all known constructions are extremely inefficient and have been shown to be insecure for some applications. The aim of this workshop is to make full use of advanced mathematical ideas, including those coming from algebraic geometry, number theory, or topology, in order to make progress on this problem and show the way towards satisfactory solutions. The plan is for the working groups to have a mixture of expertise from mathematics and computer science, and also from the cryptographic and cryptanalytic sides, to make sure that proposed solutions survive the tests of being both efficient and secure.

### Workshop on "General Relativity and AdS/CFT"

Meeting Type: Workshop

Contact: Spiro Karigiannis

### Description

This workshop will run over two weeks, Monday to Friday each week.

See website for more details and for registration.

### Automorphic Forms, Mock Modular Forms and String Theory

Meeting Type: conference

Contact: see conference website

### Description

The main objective of this workshop is to gather physicists and mathematicians working on automorphic forms, mock modular forms, black holes and moonshine in an effort to foster cross-fertilisations between these different fields. Over the last few years there have been numerous conferences devoted to the connection between mock modular forms, moonshine and string the- ory, but at these meetings the community of mathematicians working on automorphic forms and automorphic representations is usually absent. It is also our impression that mathematicians working on the Langlands program are usually unaware that many similar structures occur naturally in string theory. Thus, this proposed meeting will be dedicated to stimulating the exchange of ideas and perspectives coming from these seemingly disparate fields. This will focus parallel research activities in different fields and the BIRS workshop format and the BIRS facilities provide an ideal environment for this endeavor.

Specifically, the workshop will focus on the following cross-disciplinary areas:

• The connection between string theory amplitudes and small automorphic representations. The most supersymmetric string theory scattering processes have been interpreted as very small auto- morphic representations. Less supersymmetric processes call for an in-depth study of increasingly larger automorphic representation.

• Representation theoretic aspects of mock modular forms. Classical modular forms have a natural interpretation in terms of representation theory of reductive groups. What about mock modular forms?

• Automorphic forms on Kac-Moody groups and their relation with string amplitudes in low dimensions. The theory of automorphic forms on Kac-Moody groups and especially their Fourier ex- pansion needs to be developed further for understanding low-dimensional string theory amplitudes.

• Mock modular forms and Siegel modular forms in umbral moonshine. Umbral moonshine gives rise to a rich family of Jacobi forms and mock modular forms. Jacobi forms can be lifted to Siegel modular forms. What is the corresponding lift of the associated mock modular forms?

• Connections between umbral moonshine and Calabi-Yau compactifications of string theory. A proper string theory understand- ing of Mathieu or umbral moonshine in terms of a an underlying con- formal field theory is currently lacking.

• Automorphic representations and black hole counting. Understanding the microscopic origin of the entropy of a black hole requires counting black hole states in string theory. Since the same states also contribute to the Fourier expansion of automorphic forms, the counting problem could be rephrased in automorphic terms.

### Interplay between Number Theory and Analysis for Dirichlet Series

Meeting Type: invitational conference

Contact: see conference website

### Description

```
Organisers
```

Frédéric Bayart, Aubière

Kaisa Matomäki, Turku

Eero Saksman, Helsinki

Kristian Seip, Trondheim

## November 2017

### Minischool on "Mean Curvature Flow and Ricci Flow"

Meeting Type: Minischool

Contact: Spiro Karigiannis

### Description

This two-day minischool will serve to prepare graduate students, postdoctoral fellows, and other researchers less familiar with geometric flows for the five-day workshop on Mean Curvature Flow and Ricci Flow, immediately following, on Nov 6-10. Speakers and tentative titles:

Registration information will appear soon on the minischool website.

### Special Session in Homotopy Theory

Meeting Type: Special Session

Contact: Jonathan Beardsley

### Description

Special session in homotopy theory at the AMS Western Sectional Meeting.

### Workshop on "Mean Curvature Flow and Ricci Flow"

Meeting Type: Workshop

Contact: Spiro Karigiannis

### Description

See website for more details and for registration.

### Arithmetic and Complex Dynamics

Meeting Type: conference

Contact: see conference website

### Description

This workshop will bring together leading researchers from complex dynamics, non-Archimedean analysis and geometry, and algebraic and arithmetic geometry, with the goal of making progress on current problems in arithmetic dynamics. Recent breakthroughs have come from groups of mathematicians whose backgrounds span these varied disciplines. We will focus on sharing ideas and tools among researchers from diverse specialties in hopes of inspiring new questions and collaborations in arithmetic dynamics.

Arithmetic dynamics is an exciting and relatively new field, with many significant recent developments, so we plan to include a considerable number of young researchers. Our intended list of participants also includes a number of experts in complex dynamics and arithmetic geometry, since much of arithmetic dynamics concerns the connections between these two fields. For instance, the recent work on unlikely intersections in complex dynamics originated with a collaboration between non-Archimedean analyst Baker and complex dynamicist DeMarco, inspired by questions of arithmetic geometers Poonen, Masser, and Zannier. The workshop will sustain these extant collaborations, and found new cross-discipline research groups. To encourage this, the workshop will include casual open problem sessions on selected evenings during the week, and a speaker schedule that allows for interaction and discussion between talks.

We believe that the diverse group of researchers at the workshop will inspire many new questions in arithmetic dynamics and related fields; however, the workshop will focus on three main areas of research to guide the talks and open problem sessions.

Objective 1 (Unlikely intersections).} Bring participants up to date on recent progress in unlikely intersections in complex dynamics and in Diophantine geometry, and discuss the technical obstacles which must be overcome for future research, for example, towards developing a clean, well-formulated dynamical Andr\'e-Oort conjecture. Also of primary interest will be possibilities towards proving higher-dimensional versions of this conjecture, since all proved cases to date concern 1-dimensional varieties. Current results in this direction include progress on the dynamical analogs of well-known conjectures in arithmetic geometry, such as Mordell-Lang, Manin-Mumford, and Andr\'e-Oort [BD, BGT,Xie:DML, DF, GTZ, DWY, GKN, GKNY, GHT}. The dynamical proofs use a rich collection of techniques which include the deep equidistribution theorems of~\cite{BR, CL, FRL, YZ, Zhang:ICM], classical techniques of complex analysis and potential theory, and Ritt's theory of decomposition of polynomials, and are all illustrative of the general principle of unlikely intersections in arithmetic geometry, as in \cite{Andre, BMZ, O.

Objective 2 (non-Archimedean geometry/analysis).} Discuss the status of equidistribution theorems in various contexts, building on work of \cite{FRL, BR, CL, YZ, and the earlier ideas of Szpiro-Ullmo-Zhang, used to study abelian varieties. We now that we understand that weaker hypotheses are needed for various applications, and also that equidstribution does not always hold, even for "nice" height functions. As examples, there is the recent (non-dynamical) work of Rivera-Letelier, Burgos Gil, Philippon, and Sombra, studying the equidistribution on toric varieties, and the dynamical example of DeMarco, Wang and Ye showing that a desired ``adelic metrized line bundle" in the sense of Zhang is not always adelic. The existing equidistribution theorems have been used in many dynamical applications recently.

Objective 3 (Heights in arithmetic dynamics).} The concept of height plays a key role in arithmetic geometry, for example in Falting's proof of the Mordell conjecture and the proof of the Bogomolov conjecture by Szpiro-Ullmo-Zhang. In arithmetic dynamics, they are everywhere. Given a rational self-map of a projective variety defined over a number field, Silverman has formulated several conjectures that relate the asymptotic growth of the height along the orbit to quantities such as the dynamical degrees of the map. Special cases of these conjectures were recently proved in~\cite{Silverman:canheights, KS13,KS14,JW,JR. The workshop will feature new developments in this area, as well as related topics such as heights for finitely generated extensions of the rational numbers as studied by Moriwaki or Yuan-Zhang.

### ECC 2017: 21st Workshop on Elliptic Curve Cryptography

Meeting Type: conference

Contact: see conference website

### Description

ECC is the annual workshop dedicated to the study of elliptic-curve cryptography and related areas of modern cryptography, for more information, also about past editions of ECC, please see the main ECC website. The 21st Workshop on Elliptic Curve Cryptography (ECC 2017) will take took place on November 13–15, 2017, in Nijmegen, The Netherlands. The workshop is accompanied by a 3-day "summer" school on elliptic curves aimed at getting graduate students involved in the area. The "summer" school will take take place on November 9–11, 2017. The aim of ECC is to bring together leading experts from academia, industry, and government, as well as young researchers and graduate students for the purpose of exchanging ideas and presenting their work. The ECC Workshops has invited presentations only. Presentations tend to give an overview on emerging or established areas of modern cryptography, often combined with new research findings and often lead to new collaborations between attendees.

### Algebraic Geometry with "Fancy" Coefficients

Meeting Type: Conference

Contact: Daniele Turchetti, Jérôme Poineau

### Description

The aim of the conference is to bring together young researchers and experts of recent developments of arithmetic geometry. Topics include geometry over finite fields, Diophantine geometry, nonarchimedean phenomena and covers of curves.

Some of the talks will have a special format, with a 45 minutes introduction aiming to introduce young mathematicians to the tools that will be used in the main part of the talk. This will allow all participants to engage with topics that are not directly related to their research.

### Winter school: Categorification, representation theory and symplectic geometry

Meeting Type: Winter school

Contact: Anne-Laure Thiel, Daniel Tubbenhauer

### Description

There is a fruitful interplay between categorification, representation theory and symplectic geometry, and our intention is to highlight some of them in detail.

We hope to bring together researchers as well as students who want to learn more about the various presented aspects of the broad fields categorification, representation theory and symplectic geometry.

Please make sure that you register due to seats constraints. (Application deadline is the 31th of July 2017.)

### Workshop: Categorification, representation theory and symplectic geometry

Meeting Type: Workshop

Contact: Anne-Laure Thiel, Daniel Tubbenhauer

### Description

There is a fruitful interplay between categorification, representation theory and symplectic geometry, and our intention is to highlight some of them in detail.

We hope to bring together researchers as well as students who want to learn more about the various presented aspects of the broad fields categorification, representation theory and symplectic geometry.

Please make sure that you register due to seats constraints. (Application deadline is the 31th of July 2017.)

## December 2017

### Algebraic Geometry and Number Theory

Meeting Type: conference

Contact: see conference website

### Description

This conference will be on various topics in algebraic geometry, number theory and interplay between them.

## January 2018

### Periods in Number Theory, Algebraic Geometry and Physics

Meeting Type: conference

Contact: see conference website

### Description

he word "period" is used to designate any number represented by the integral of an algebraic differential form over a cycle in an algebraic variety over \mathbb{Q} (or \overline{\mathbb{Q}}). These include many numbers of interest in number theory and mathematical physics (multiple zeta values, Mahler measures, superstring amplitudes, ...), and also have deep connections with special values of motivic L-functions.

The trimester will be divided into five "activities", each concentrating on one topic and including one or several introductory courses, and also three one-week workshops featuring lectures on current work:

```
Motives and Periods (Jan 3 - Jan 14)
Workshop: Periods and Regulators (Jan 15 - Jan 19)
Regulators (Jan 20 - Feb 4)
Amplitudes (Feb 5 - Feb 25)
Workshop: Amplitudes and Periods (Feb 26 - Mar 2)
Picard-Fuchs Equations and Geometry (Mar 3 - Mar 25)
Workshop: Picard-Fuchs Equations and Hypergeometric Motives (Mar 26 - Mar 30)
Hypergeometric Motives (Mar 31 - Apr 20)
```

### Singularities and Algebraic Geometry

Meeting Type: conference

Contact: Nero Budur (KU Leuven), Le Quy Thuong (VNU), Nguyen Hong Duc (BCAM), Pho Duc Tai (VNU)

### Description

The conference is dedicated to recent advances in Algebraic Geometry and Singularities.

### Model theory, combinatorics and valued fields

Meeting Type: thematic program

Contact: see conference website

### Description

Model theory is a branch of mathematical logic which deals with the relationship between formal logical languages (e.g. first order logic, or variants such as continuous logic) and mathematical objects (e.g. groups, or Banach spaces). It analyses mathematical structures through the properties of the category of its definable sets. Significant early applications of model theory include Tarski's decidability results in the 1920s (algebraically closed fields, real closed fields), and in the 1960s the well-known Ax-Kochen/Ershov results on the model theory of Henselian valued fields.

These last few years have seen an extremely rapid development of the powerful tools introduced for stable structures in a much larger context, that of “tame” structures. Our main themes for this programme aim to develop both the internal model theory of tame structures and their recent applications.

The programme will bring together researchers on the following topics:

(i) Model theory and application to combinatorics. Additive combinatorics (approximate subgroups and variations); Around Szemerédi Regularity Lemma and Density Theorem; Pseudofinite structures (e.g., ultraproducts of finite structures); Vapnik-Chervonenkis theory, applications, and NIP theories; Continuous model theory; Generalised stability theory and tame structures. (ii) Model theory of valued fields and applications. The prime focus is on the model theory of Henselian valued fields with the valuation topology, often with extra structure and under assumptions which ensure that definable sets can be understood. Motivic integration; Algebraically closed valued fields, imaginaries, and Berkovich spaces; Valued fields with additional structure; Transseries and surreal numbers; Definable groups. (iii) Applications of model theory in geometry, analysis and number theory. Study of fields with operators and their applications to concrete problems; Applications of the Pila-Wilkie counting theorem.

The emphasis will be on the first two themes, where interactions and collaborations are still at an early stage. Theme (iii) is already well developed, and has connections with both themes (i) and (ii), mainly through concrete algebraic examples. While very present in the programme, it is less central.

We intend to concentrate the activities of theme (i) (around Combinatorics) in the period 15 January - 9 February, leading up to and including the first meeting, and those of theme (ii) (around valued fields) in the period 12 February - 9 March, leading up to and including the second meeting. The third and final meeting will be general, including all three themes. However, we expect to have people from all themes of the programme at any point of time.

### Riemann-Hilbert correspondences

Meeting Type: summer school, workshop

Contact: see conference website

### Description

Recent groundbreaking developments in the theory of irregular holonomic D-modules have brought to light new relationships among D-module theory and other subjects such as Non Commutative Hodge theory, Mirror Symmetry and Microlocal Analysis. The aim of this event is twofold: to provide an introduction to this new active area for young students and researchers (4 courses on previous developments will be delivered during the first week), and to present the state of the art on the subject (several talks by top international experts are scheduled for the second week). Research talks by young participants are also scheduled during the first week.

## March 2018

### The Homological Conjectures: Resolved!

Meeting Type: conference

Contact: see conference website

### Description

The homological conjectures in commutative algebra are a network of conjectures that have generated a tremendous amount of activity in the last 50 years. They had largely been resolved for commutative rings that contain a field, but, with the exception of some low dimensional cases, several remained open in mixed characteristic --- until recently, when Yves Andr\'e announced a proof of Hochster's Direct Summand Conjecture. The progress comes from systematically applying Scholze's theory of perfectoid spaces, which had already shown its value by solving formidable problems in number theory and representation theory. One of the goals of the workshop is to cover the ingredients going into the proofs of the Direct Summand Conjecture.

### Picard-Fuchs Equations and Hypergeometric Motives

Meeting Type: conference

Contact: see conference website

### Description

## April 2018

### Algebraic Groups and Geometrization of the Langlands Program

Meeting Type: thematic program

Contact: see conference website

### Description

A thematic trimester in arithmetic will take place in ENS de Lyon and Université Lyon 1 from April 23, 2018 to June 29, 2018. This trimester is divided in two parts with different focus, with a conference taking place from May 22 to May 25.

The first part of the trimester focuses on the theory of algebraic groups, and particularly the Grothendieck-Serre conjecture on locally trivial homogeneous principal spaces. The conjecture was proved by Fedorov and Panin, following work of Colliot-Thélène, Nisnevich, Ojanguren, Ragunathan, Stavrowa, Vavilov...In the arithmetic case, Fedorov proved recently a significant special case of the conjecture. The study of this problem uses, among others, approximation techniques in algebraic groups, patching techniques, and affine grassmanians.

The second part of trimester focuses mainly on the question of the geometrization of the local Langlands correspondence. This problem was born from three major advances in arithmetic geometry: the introduction of the theory of perfectoid spaces by Scholze, the work of V. Lafforgue on the Langlands correspondence for function fields, and the introduction by Fargues and Fontaine of the fundamental curve of p-adic Hodge theory. We will take stock of the latest advances.

## May 2018

### Birational Geometry and Arithmetic

Meeting Type: conference

Contact: Sho Tanimoto

### Description

### Rational and Integral Points via Analytic and Geometric Methods

Meeting Type: conference

Contact: see conference website

### Description

## June 2018

### Arithmetic and Algebraic Geometry - a conference in honor of Ofer Gabber on the occasion of his 60th birthday

Meeting Type: conference

Contact: Ahmed Abbes

### Description

### Algebraische Zahlentheorie

Meeting Type: invitational workshop

Contact: see conference website

### Description

Organisers

- Guido Kings, Regensburg
- Ramdorai Sujatha, Vancouver
- Eric Urban, New York
- Otmar Venjakob, Heidelberg

## July 2018

### Higher structures in homotopy theory

Meeting Type: conference

Contact: Clark Barwick, Julie Bergner, Ieke Moerdijk, Stefan Schwede, Paul Goerss

### Description

Part of the Semester Programme "Homotopy Harnessing Higher Structures". This programme will highlight four related themes: the new algebraic topology of differentiable manifolds, derived representation theory and equivariant homotopy theory, the interplay between arithmetic geometry and stable homotopy theory, and the analysis of foundations in these new contexts "the homotopy theory of homotopy theory". This particular workshop will focus on the last of these themes.

### Canadian Number Theory Association Conference (CNTA XV) -- Laval University

Meeting Type: conference

Contact: Hugo Chapdelaine, Antonio Lei, Claude Levesque

### Description

The Canadian Number Theory Association (CNTA) was founded in 1987 at the International Number Theory Conference at Laval University (Quebec), for the purpose of enhancing and promoting learning and research in number theory, particularly in Canada. To advance these goals, the CNTA organizes bi-annual conferences that showcase new research in number theory, with the aim of exposing Canadian and international students and researchers to the latest developments in the field. The CNTA meetings are among the largest number theory conferences world-wide.

### Algorithmic Number Theory Symposium ANTS-XIII

Meeting Type: conference

Contact: see conference website

### Description

### Explicit Methods in Number Theory

Meeting Type: invitational workshop

Contact: see conference website

### Description

Organisers

- Karim Belabas, Bordeaux
- Bjorn Poonen, Cambridge MA
- Fernando Rodriguez Villegas, Trieste

### 2018 ICM satellite conference in Number Theory

Meeting Type: conference

Contact: Henri Darmon, Fred Diamond, Kiran Kedlaya, Aftab Pande, Richard Taylor, Marie-France Vigneras

### Description

Automorphic forms, Galois representations and L-functions, and the interplay among them, have been at the heart of numerous major advances in number theory over the last few decades, from their relevance to long-standing problems such as Fermat's Last Theorem and the Birch and Swinnerton-Dyer Conjecture to their role in the evolution of new research directions such as the the p-adic Langlands program and the theory of perfectoid spaces. The conference will focus on recent developments, with topics that include the Langlands program, special values of L-functions, Shimura varieties and p-adic Hodge theory.

## August 2018

### International Congress of Mathematicians

Meeting Type: international congress

Contact: see conference website

### Description

Satellite conferences will appear later with their own entries.

### Equivariant and motivic homotopy theory

Meeting Type: workshop

Contact: John Greenlees, Lars Hesselholt, Mike Hill, Dan Isaksen, Paul Goerss

### Description

Part of the Semester Program "Homotopy Harnessing Higher Structures." This programme will highlight four related themes: the new algebraic topology of differentiable manifolds, derived representation theory and equivariant homotopy theory, the interplay between arithmetic geometry and stable homotopy theory, and the analysis of foundations in these new contexts "the homotopy theory of homotopy theory". This workshop will focus on equivariant homotopy theory and its applications.

## September 2018

### Varieties: Arithmetic and Transformations

Meeting Type: conference

Contact: see conference website

### Description

Focus points

- Group actions: Mori Dream Spaces, $T$-varieties, also toric varieties, homogeneous spaces, contact Fano manifolds, Cremona groups, actions of finite groups, $\mathbb{G}_a$ and $\mathbb{G}_m$ actions on affine varieties,
- Arithmetic: arithmetic aspects of differential equations, $p$-adic cohomologies, crystals, automorphic forms, Calabi-Yau varieties, arithmetic aspects of mirror symmetry, finding rational points on manifolds,
- Parametrizing varieties: Hilbert scheme of points, rational curves on manifolds, secant varieties, tensor ranks, Waring ranks and related notions with their applications to complexity theory, engineering and quantum physics

### Derived algebraic geometry and chromatic homotopy theory

Meeting Type: conference

Contact: Mark Behrens, David Gepner, Paul Goerss, Mike Hopkins, Tyler Lawson,

### Description

Part of the Semester Program "Homotopy Harnessing Higher Structures." This programme will highlight four related themes: the new algebraic topology of differentiable manifolds, derived representation theory and equivariant homotopy theory, the interplay between arithmetic geometry and stable homotopy theory, and the analysis of foundations in these new contexts "the homotopy theory of homotopy theory". This workshop will focus on derived algebraic geometry and the interplay with stable homotopy theory.

### Special Values of Automorphic L-functions and Associated p-adic L-Functions

Meeting Type: conference

Contact: see conference website

### Description

## December 2018

### Manifolds

Meeting Type: workshop

Contact: David Ayala, Oscar Randal-Williams, Ulrike Tillmann, Michael Weiss, Paul Goerss

### Description

Part of the Semester Program "Homotopy Harnessing Higher Structures." This programme will highlight four related themes: the new algebraic topology of differentiable manifolds, derived representation theory and equivariant homotopy theory, the interplay between arithmetic geometry and stable homotopy theory, and the analysis of foundations in these new contexts "the homotopy theory of homotopy theory". This workshop will focus on the algebraic topology of manifolds.

## January 2019

### Birational Geometry and Moduli Spaces

Meeting Type: research program

Contact: see conference website

### Description

Birational Geometry and Moduli Spaces are two important areas of Algebraic Geometry that have recently witnessed a flurry of activity and substantial progress on many fundamental open questions. In this program we aim to bring together key researchers in these and related areas to highlight the recent exciting progress and to explore future avenues of research.

This program will focus on the following themes: Geometry and Derived Categories, Birational Algebraic Geometry, Moduli Spaces of Stable Varieties, Geometry in Characteristic p>0, and Applications of Algebraic Geometry: Elliptic Fibrations of Calabi-Yau Varieties in Geometry, Arithmetic and the Physics of String Theory

### Derived Algebraic Geometry

Meeting Type: research program

Contact: see conference website

### Description

Derived algebraic geometry is an extension of algebraic geometry that provides a convenient framework for directly treating non-generic geometric situations (such as non-transverse intersections in intersection theory), in lieu of the more traditional perturbative approaches (such as the “moving” lemma). This direct approach, in addition to being conceptually satisfying, has the distinct advantage of preserving the symmetries of the situation, which makes it much more applicable. In particular, in recent years, such techniques have found applications in diverse areas of mathematics, ranging from arithmetic geometry, mathematical physics, geometric representation theory, and homotopy theory. This semester long program will be dedicated to exploring these directions further, and finding new connections.

## March 2019

### Derived algebraic geometry and its applications

Meeting Type: conference

Contact: see conference website

### Description

This workshop will bring together researchers at various frontiers, including arithmetic geometry, representation theory, mathematical physics, and homotopy theory, where derived algebraic geometry has had recent impact. The aim will be to explain the ideas and tools behind recent progress and to advertise appealing questions. A focus will be on moduli spaces, for example of principal bundles with decorations as arise in many settings, and their natural structures.

## July 2019

### Journées Arithmétiques

Meeting Type: conference

Contact: see conference website

### Description

The Journées Arithmétiques meetings, held every two years, cover all aspects of number theory. The venues alternate between locations in France and locations elsewhere in Europe.