## 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.

## March 2017

### Local zeta functions and the arithmetic of moduli spaces: A conference in memory of Jun-Ichi Igusa

Meeting Type: conference

Contact: see conference website

### Description

This meeting, sponsored by the Japan-U.S. Mathematics Institute at Johns Hopkins University, will be organized around significant recent developments in the study of:

- local zeta functions and
- the geometry and arithmetic of moduli spaces of curves and their Jacobians in low genus,

two principal areas of number theory and algebraic geometry in which Jun-Ichi Igusa made pioneering contributions. Please see the conference website for a list of confirmed speakers.

### Noncommutative Geometry

Meeting Type: conference

Contact: see conference website

### Description

### Galois theory of periods and applications

Meeting Type: conference

Contact: see conference website

### Description

Periods are integrals of algebraic differential forms over algebraically-defined domains and are ubiquitous in mathematics and physics. A deep idea, originating with Grothendieck, is that there should be a Galois theory of periods. This general principle provides a unifying approach to several problems in the theory of motives, quantum groups and geometric group theory. This conference will bring together leading experts around this subject and cover topics such as the theory of multiple zeta values, modular forms, and motivic fundamental groups.

### p-adic Analytic Geometry and Differential Equations

Meeting Type: conference

Contact: see conference website

### Description

The subject of p-adic analytic geometry has been booming in the last years, as regards foundational matters as well as applications. In particular, the use of fine methods from analytic geometry in the field of p-adic differential equations and D-modules has recently led to significant progress. The aim of the conference is to bring together mathematicians from various areas around those themes, experts as well as new-comers who would like to incorporate them into their research. The atmosphere at CIRM will encourage fruitful discussion and collaboration between the communities in presence.

## April 2017

### Arbeitsgemeinschaft: Higher Gross Zagier Formulas

Meeting Type: learning conference

Contact: see conference website

### Description

The “Arbeitsgemeinschaft Deninger-Faltings” is a series of meetings in Oberwolfach taking place each year in spring and fall. The topic of the next meeting is chosen by democratic vote. The stay at Oberwolfach is free.

The Arbeitsgemeinschaft (study group) mainly addresses to non-specialists who want to broaden their outlook on mathematics and to young mathematicians who wish to enter a field for future research. Experts are also welcome. The idea is “learning by doing” – similar to the Seminaire Bourbaki. Participants have to volunteer for one of the lectures described in the program of the Arbeitsgemeinschaft. After the deadline for application the organizers choose the actual speakers to give them enough time to understand the subject and to prepare for their lectures. Please see our website www.mfo.de for further details.

The MFO is grateful to Prof. Dr. Christopher Deninger (Münster) and Prof. Dr. Gerd Faltings (MPI Bonn) who lead the Arbeitsgemeinschaft.

### Young Women in Geometry

Meeting Type: workshop

Contact: see conference website

### Description

This meeting is part of the series of workshops Young Women in...

The main lectures will be given by

```
Anna Wienhard
Esther Cabezas-Rivas
Julie Rowlett
```

The workshop provides a platform for female graduate students and postdocs in Geometry to present their research. The main lectures will be complemented by participants' talks and a poster exhibition.

Everybody is welcome to attend the workshop. We encourage all participants - male and female - to contribute a poster to our poster sessions and to apply for a contributed talk.

Organizers: Asma Hassannezhad, Anna Siffert

### Invertible Objects and Duality in Derived Algebraic Geometry and Homotopy Theory

Meeting Type: conference

Contact: Martha Hofmann, Justin Noel

### Description

The aim of this conference is to present recent advances related to the study of invertible objects, duality, and higher invariants in derived algebraic geometry and homotopy theory. In particular, this conference will include talks on the recent breakthroughs in the study of units, Picard groups, Brauer groups, twists, and module categories. The activity will consist of a four-part lecture series as well as a number of invited lectures. There will also be an opportunity for junior participants to make short presentations.

### The Third mini symposium of the Roman Number Theory Association

Meeting Type: conference

Contact: Valerio Talamanca

### Description

The Roman Number Theory Association in collaboration with Roma Tre University and Universita' Europea di Roma, organises yearly a one-day symposia.

Speakers:
Lucia Di Vizio* (Université Versailles-St Quentin)

Andrew Granville (University College London)

Alessandro Languasco (Università di Padova)

Christian Maire (Université Franche-Comté)

Pieter Moree* (Max-Plank Institute fur Mathematics)

Alberto Perelli (Università di Genova)

René Schoof (Università di Roma Tor Vergata)

Peter Stevenhagen (Universiteit Leiden)

Fernando Rodriguez Villegas (ICTP)

Michel Waldschmidt (Université Pierre et Marie Curie)

*= to be confirmed

### 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.

### Hodge theory, Stokes Phenomenon and Applications

Meeting Type: conference

Contact: see conference website

### Description

The project of this conference takes place in the framework of the SISYPH program, an joint ANR (France) -DFG (Germany) program. It is intended to give the state of the art concerning the results obtained during the 3-year period of SISYPH, both by SISYPH members and by other researchers who brought a substantial contribution to the following topics:

- Mirror symmetry as an efficient tool for the computation of various Gromov-Witten invariants for smooth algebraic varieties and orbifolds.
- Irregular singularities of linear differential equations in all dimensions, from the point of view of D-modules and of isomonodromic deformations.
- Hodge-theoretical properties for such differential systems.

### 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

### AGNES (Algebraic Geometry Northeastern Series)

Meeting Type: conference

Contact: see conference website

### Description

### Texas Algebraic Geometry Symposium

Meeting Type: conference

Contact: John Calabrese, Tony Várilly-Alvarado

### Description

Historically rooted in the study of solutions to polynomial equations, algebraic geometry remains in the twenty-first century a vibrant subject with both its own deep internal questions as well as far-reaching interactions with many other parts of science and mathematics. Started in 2005, TAGS is a major annual event in the regional algebraic geometry community, bringing together experts in diverse aspects of the subject as well as graduate students and postdocs just entering it.

### Teichmüller theory and mirror symmetry

Meeting Type: conference

Contact: see conference website

### Description

We propose two series of lectures by :

Misha Verbitsky on Teichmüller theory

Dimitri Zvonkine on cohomological field theory

Each morning, there will be an two hours of lectures followed in the afternoon by more advanced results by internationnal mathematicians.

Speakers:

Gaetan Borot, Max Planck Institut, Bonn Fabrizio Catanese, University of Bayreuth Amerik Ekaterina, University of Orsay (tbc) Maxim Kontsevich, IHES (tbc) Thomas Reichelt, University of Heidelberg Claude Sabbah, Ecole polytechnique Andrei Teleman, University of Aix-Marseille

Organization board: Frédéric Mangolte Etienne Mann Laurent Meersseman Alexis Roquefeuil

### Positivity in Algebraic and Complex Geometry

Meeting Type: WORKSHOP

Contact: Julius Ross

### Description

Organisers Daniel Greb Sándor Kovács Alex Küronya Julius Ross

This is an early announcement of the above workshop. We are interested in hearing from researchers and graduate students working in this area who are interested in attending. Please note that spaces may be limited so if there is a large positive response we may need to be selective. Also, at this stage most of our funding has been allocated, but more may become available in the future.

Should you be interested in this workshop please email Julius Ross (j.ross@dpmms.cam.ac.uk)

### Bridges between Automatic Sequences, Algebra and Number Theory

Meeting Type: school + workshop

Contact: see conference website

### Description

The aim of the school and workshop is to bring together graduate students, postdocs, and senior researchers working in the theory of automatic sequences or in areas that have some strong connection to automatic sequences to discuss their research and foster collaboration. The workshop will have a strong focus on the applications of automata and automatic sequences to algebra and to number theory.

As part of the Aisenstadt chair of the thematic semester, Boris Adamczewski will give a series of lectures on automatic sequences which will take place during these two weeks.

SCHOOL

The school will consist of mini-courses on topics issued from combinatorics of words, algebra and number theory. This mini-courses will cover some of the algebraic and number theoretic background that will be useful for participants of the Workshop Bridges between Automatic Sequences and Algebra and Number Theory taking place the week after.

The mini-courses of the School will be given by:

– Yann Bugeaud (Université de Strasbourg) – Christophe Reutenauer (Université du Québec à Montréal) – Reem Yassawi (Université Paris Diderot-Paris 7)

Yann Bugeaud will give a minicourse about links between factor complexity, automatic numbers, transcendance and Diophantine approximation. Christophe Reutenauer will describe the correspondence between the theory Markoff numbers and the theory of Christoffel words. Reem Yassawi will give an introduction to automatic sequences, including in particular their links with algebra and number theory.

Other talks will be given by:

– Robbert Fokkink (Delft University of Technology) – Julien Leroy (Université de Liège) – Narad Rampersad (University of Winnipeg) – Eric Rowland (Hofstra University) – Štěpán Starosta (Czech Technical University in Prague) – Élise Vandomme (Université du Québec à Montréal)

We also plan sessions of exercises or experiments on computer allowing to develop intuitions on the presented mini-courses and talks.

WORKSHOP

The theory of finite automata naturally interacts, via automatic sequences and automatic sets, with algebra and number theory. Several advances have recently reinforced these deep links. The aim of this workshop is to allow researchers from different areas to meet and exchange about these advances. Among the themes to be covered by the invited talks are: transcendence and Diophantine analysis, arithmetic in positive characteristic, Galois theory of difference and differential equations, logic and model theory, analytic number theory, combinatorics and formal power series, group theory.

### International Conference on Algebra and its Applications (ICAA-2017)

Meeting Type: conference

Contact: see conference website

### Description

Gather the national and international scientific community of the domain to allow the moroccan researchers to exchange and to develop their knowledge of search in the field of algebra and its applications. It also aims to present recent progress and new trends in algebra and its applications. This will allow the participants to enrich their ideas and their knowledge regarding search in this domain.

AREAS OF INTEREST:

The scope of the ICAA-2017 conference encompasses, but is not limited to, the following areas:

Associative algebra and its applications. Commutative algebra and its applications. Homological algebra and its applications. Number theory and its applications. Cryptography and its applications. Non-commutative algebra and its applications. Applications of algebra to real problems. This conference is organized by

Abdellah MAMOUNI Mohammed TAOUS

### JDG 2017 Conference on Geometry and Topology

Meeting Type: conference

Contact: see conference website

### Description

The conference will also mark the special occasion of the 50th anniversary of the publication of Journal of Differential Geometry (1967-2017).

Confirmed Speakers:

Mina Aganagic (UC Berkeley) Dennis Auroux (UC Berkeley) Caucher Birkar (University of Cambridge) Huai-Dong Cao (Lehigh University) Tristan Collins (Harvard University) Camillo De Lellis (University of Zurich) Jean-Pierre Demailly (Grenoble) Simon Donaldson (Simons Center, Stony Brook) Dan Freed (UT Austin) Kenji Fukaya (Simons Center, Stony Brook) David Gabai (Princeton University) Larry Guth (MIT) Richard Hamilton (Columbia University) Yujiro Kawamata (University of Tokyo) Frances Kirwan (University of Oxford) Blaine Lawson (Stony Brook) Jun Li (Stanford University) Si Li (Tsinghua University, Beijing) Bong Lian (Brandeis University) Melissa Liu (Columbia University) Kefeng Liu (UCLA) Ciprian Manolescu (UCLA) Fernando Marques (Princeton University) William Meeks (University of Massachusetts) William Minicozzi (MIT) John Pardon (Princeton University) Duong Phong (Columbia University) Alena Pirutka (Courant, NYU) Richard Schoen (UC Irvine) Cliff Taubes (Harvard University) Cumrun Vafa (Harvard University) Mu-Tao Wang (Columbia University) Steve Zelditch (Northwestern University)

### O-Minimality and its Applications to Number Theory and Analysis

Meeting Type: invitational conference

Contact: see conference website

### Description

```
Organisers
```

Tobias Kaiser, Passau

Jonathan Pila, Oxford

Patrick Speissegger, Hamilton

Alex Wilkie, Manchester

## May 2017

### A View Toward Algebraic Geometry

Meeting Type: conference

Contact: Daniel Erman, Mircea Mustaţă , Claudiu Raicu , Gregory G. Smith,

### Description

### Recent developments in analytic number theory

Meeting Type: conference

Contact: see conference website

### Description

This workshop will be focused on presenting the latest developments in analytic number theory, including (but not restricted to) recent advances in sieve theory, multiplicative number theory, exponential sums, arithmetic statistics, estimates on automorphic forms, and the Hardy-Littlewood circle method.

### Journées Complexes Lorraines 2017

Meeting Type: conference

Contact: see conference website

### Description

Invited Speakers:

Joseph Ayoub

Damian Brotbek

Yohan Brunebarbe

François Charles

Julie Déserti

Pascal Dingoyan

Henri Guenancia

Florian Ivorra

Christian Lehn

Manfred Lehn

Christophe Mourougane

Dan Popovici

Behrouz Taji

Frédéric Touzet

Charles Vial

Jaroslaw Wisniewski

If you'd like to participate please register before April 7th by writing to one of the organizers using an e-mail address of the type:

forename.name@univ-lorraine.fr

Our budget allows us to support travel or accommodation costs for a certain number of young participants. Please mention in your registration mail if you need such support.

Organizing committee

Frédéric Campana

Benoît Claudon

Damien Mégy

Gianluca Pacienza

Arvid Perego

Matei Toma

### Seventh Upstate New York Number Theory Conference

Meeting Type: conference

Contact: Alexander Borisov

### Description

This is the seventh installment of the Upstate NY Number Theory Conference, that rotates among Cornell, Rochester, Binghamton, and Buffalo. This year's conference has a broad scope. Our aim is to bring together the specialists from the various branches of Number Theory, and to expose the younger researchers to new and old problems in the field.

### Simons Symposium: P-adic Hodge Theory

Meeting Type: invitational workshop

Contact: see conference website

### Description

Organized by Bhargav Bhatt (University of Michigan) and Martin Olsson (UC Berkeley), the symposium will bring together experts to explore recent developments in p-adic Hodge theory and understand the emerging relationship of p-adic Hodge theory with other subjects in mathematics. The topics to be discussed include:

```
The relationship between p-adic Hodge theory, algebraic K-theory, and topological Hochschild homology.
Recent developments in integral p-adic Hodge theory.
The connection between p-adic Hodge theory and derived algebraic geometry.
```

### 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.

### Distribution of modular symbols and L-values: computations and applications

Meeting Type: conference

Contact: see conference website

### Description

The goal of the workshop is to try to begin to understand the growth of Mordell-Weil groups of elliptic curves in infinite abelian extensions, using heuristics and calculations.

### Simons Symposium: Non-Archimedean and Tropical Geometry

Meeting Type: invitational workshop

Contact: see conference website

### Description

Organized by Matthew Baker (Georgia Tech) and Sam Payne (Yale University), the symposium will focus on setting a clear agenda for future developments in the related fields of tropical and non-Archimedean analytic geometry. One of the meeting goals is to produce high quality expository material presenting the methods, results and ambitions of these active research areas. Another is to identify problems in other fields of mathematics that could be amenable to tropical and non-Archimedean analytic methods and establish new rigorous links with those neighboring fields. Discussion Topics Include:

```
Combinatorial and tropical analogues of Hodge theory
Refined curve counting, tropical geometry, and motivic invariants
Wild coverings of curves and lifting problems for algebraic and tropical curves
Rational points on curves, p-adic integration, and relations with tropical geometry
```

### Modular Forms are Everywhere

Meeting Type: conference

Contact: see conference website

### Description

### Geometry of Moduli Spaces

Meeting Type: conference

Contact: Dragos Oprea

### 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

### 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

### 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

### 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.

### 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)
```

### 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

### 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.

### 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.

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

Meeting Type: conference

Contact: see conference website

### Description

### 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.

### Arithmetic Geometry and Computer Algebra

Meeting Type: workshop

Contact: Jan Steffen Müller

### Description

## July 2017

### 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
```

### 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

### 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

### Sage Days 87: p-adics+

Meeting Type: software development workshop

Contact: see conference website

### Description

### 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.

### 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.

### 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.

### 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

### 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.

### 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

### 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

### 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.

## 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

```
[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.

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### 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

### 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.

## 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.

## 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.

## 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

### 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.

## 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

## 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.

## 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.