## 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

## October 2016

### Oberwolfach Seminar: Perfectoid Spaces

Meeting Type: graduate school

Contact: Kiran Kedlaya, Jared Weinstein

### Description

### Definability and Decidability Problems in Number Theory

Meeting Type: conference

Contact: see conference website

### Description

Hilbert’s tenth problem (H10 for short) asked for an algorithm to decide solvabil- ity of Diophantine equations in the integers. Building on work of M. Davis, H. Putnam and J. Robinson, Matiyasevich showed in 1970 that every recursively enumerable set can be realized as a Diophantine set, and therefore H10 has a negative answer. This result did not resolve the analogous decidability question for Q, other number fields, or their rings of integers. In 1949, using the first-order undecidability of Z (already known by then), Julia Robinson succeeded in showing that the full theory of Q was undecidable by constructing a first-order definition of Z in Q. Similarly, an existential definition of Z in Q would provide a negative solution to the ana- logue of H10 over Q. The search for such a definition or a proof that it does not exist is a major theme within the subject. In the fifties, Julia Robinson initiated the study of definability and decidability over number fields and infinite algebraic extensions of Q, while Raphael Robinson took the first steps towards the understanding of the first-order theory over function fields and analytic structures.

In the last 20 years or so, considerable progress has been achieved on these problems thanks to the discovery of striking connections with other fields of mathematics, such as algebraic ge- ometry, anabelian geometry, Nevanlinna theory and recursion theory. However, many funda- mental questions remain wide open due to our lack of understanding of Diophantine sets. This workshop will serve as an opportunity for researchers in related fields to bring together their ideas and expertise in order to make progress on these matters, and to make more widely known the techniques and recent developments in the area.

### Conference in the honour of Said Zarati

Meeting Type: conference

Contact: see conference website

### Description

**This is a conference in algebraic topology celebrating Said Zarati's 65th birthday.**

Registration is now open.

**About Said Zarati**

Saïd Zarati is a mathematician, specializing in Algebraic Topology, who studied at Tunis El Manar University then at Paris-Sud University where he defended his "thèse d'Etat" under the supervision of Jean Lannes. Back to Tunisia, he was appointed "Maître de Conférences" (1984) then Professor at Tunis El Manar University (1999).

He is an internationally recognized expert in the theory of unstable modules over the Steenrod algebra whose growth was boosted at the beginning of the eighties by works on the Sullivan conjecture. In particular, using the interactions between this theory and commutative algebra, he proved in 1996, jointly with Dorra Bourguiba, the Landweber-Stong conjecture about the depth of certain rings of invariants.

Saïd Zarati has founded a research unit in algebraic topology at the Faculty of Sciences of Tunis (FST) and is today the head of the research laboratory LATAO. He has supervised several Masters and Ph.D. theses; and his students (from all academic levels) have widely acclaimed his teaching skills.

He was Chairman of the Department of Mathematics of the FST for quite a while and has always been very active within the Tunisian Mathematical Society of which he was a founding member.

### Second NZ Number Theory Workshop

Meeting Type: conference

Contact: Felipe Voloch

### Description

### Rutgers Geometric Analysis Conference 2016

Meeting Type: conference

Contact: Paul Feehan, Natasa Sesum

### Description

Our two-day conference highlights recent developments in analysis of non-linear elliptic and parabolic partial differential equations arising in differential geometry and geometric flow equations --- including mean curvature flow, Ricci flow, and Yang-Mills gradient flow. The Friday Workshop features leading experts in geometric analysis while the Thursday Mini-Courses are intended to introduce Ph.D. students and junior mathematicians to key concepts in geometric analysis.

There is no fee to participate in the conference, but **registration is required** of all participants in order to ensure adequate facilities for attendees and for anonymous reporting of attendance numbers to the National Science Foundation.

### Low Dimensional Topology and Quantum Algebra

Meeting Type: conference

Contact: Scott Morrison

### Description

Although in the past they have been viewed as separate fields, low-dimensional topology and quantum algebra have recently seen surprising interactions with the development of new topological invariants with deep connections to quantum groups and category theory. These invariants have proven to be effective tools for tackling fundamental problems in manifold and link theory, but they also have generated new research activity in algebra due to their compelling internal structure with close connections to higher categories and higher representation theory. This workshop will focus on recent advances in this developing subject, bringing together researchers from all parts of this vibrant field, and highlighting work of both established experts and exceptional young researchers from inside and outside of Australia.

## November 2016

### Fields Institute Symposium: Manjul Bhargava

Meeting Type: conference

Contact: see conference website

### Description

The 2016 Fields Medal Symposium will be centered on the work of Manjul Bhargava (Fields Medal 2014), and its current and potential impact.

The scientific program is aimed at a wide audience, including graduate students, mathematicians in other research areas, and scientists who use mathematics in an important way. The public opening lecture of the Symposium (November 1, 2016) will feature a lecture for a general audience given by Manjul Bhargava. The Symposium will also have a special event for high school and undergraduate students. All events will be broadcast live online.

### AGNES (Algebraic Geometry Northeastern Series)

Meeting Type: conference

Contact: see conference website

### Description

AGNES is a series of weekend workshops in algebraic geometry. One of our goals is to introduce graduate students to a broad spectrum of current research in algebraic geometry. AGNES is held biannually at the participating universities in the Northeast.

### Texas Geometry and Topology Conference

Meeting Type: conference

Contact: see conference website

### Description

The 56th meeting of the Texas Geometry and Topology Conference will be held at Texas A&M University, November 4-6, 2016.

Speakers

- Anna Marie Bohmann, Vanderbilt
- Robert Hardt, Rice University
- Vaughan Jones, Vanderbilt
- Niky Kamaran, McGill
- Shrawan Kumar, UNC Chapel Hill
- Rafe Mazzeo, Stanford University
- Emmy Murphy, MIT
- Thomas Schick, U. Goettingen

This conference is supported by the National Science Foundation and Texas A&M University. There are no registration fees. Everyone is welcome. Some support is available. Graduate students, post-docs, junior faculty, women, minorities, and persons with disabilities are especially encouraged to participate and to apply for support. For conference information, see the conference web page at http://www.math.tamu.edu/conferences/tgtc/2016/ .

### Analytic Number Theory

Meeting Type: conference

Contact: see conference website

### Description

### Homological Mirror Symmetry: Methods and structures

Meeting Type: workshop

Contact: see conference website

### Description

This is one of two workshops during a year-long program.

During the 2016-17 academic year, the School will have a special program on Homological Mirror Symmetry. Paul Seidel, from MIT, will be the Distinguished Visiting Professor. Maxim Kontsevich, from IHES, will be attending the program for one month during each of the fall and spring terms (from mid-October to mid-November, and for the month of February). Denis Auroux, from UC Berkeley, will be attending for the spring term.

### Conformal Geometry and Spectral Theory

Meeting Type: conference

Contact: Florin Belgun

### Description

Intended as a celebrating event of Andreas Juhl's 60th birthday, the conference will bring together researchers from various areas of conformal geometry and spectral theory and aims to encourage cooperations between them, as well as to underline the impact of these topics in related areas of differential geometry.

Invited speakers:

- Bernd Ammann (University of Regensburg)
- Fran Burstall (University of Bath)
- Andreas Čap (University of Vienna)
- Matthias Fischmann (Aarhus University)
- Charles Frances (University of Strasbourg)
- Robin Graham (University of Washington)
- Matthias Hammerl (University of Greifswald)
- Paweł Nurowski (Polish Academy of Sciences, Warsaw)
- Martin Olbrich (University of Luxembourg)
- Bent Ørsted (Aarhus University)
- Michael Pevzner (University of Reims)
- Jan Slovák (Masaryk University Brno)

### Virginia Topology Conference 2016: Mapping class groups and low dimensional topology

Meeting Type: conference

Contact: see conference website

### Description

### 57th Cascade Topology Seminar

Meeting Type: conference

Contact: Allison Henrich

### Description

We are happy to announce the 57th Cascade Topology Seminar, to be held at Seattle University on November 19th and 20th, 2016.

Speakers for the Cascade Topology Seminar include:

- Louis Kauffman, University of Illinois Chicago
- Ryan Derby-Talbot, Quest University Canada
- Marion Campisi, San Jose State University
- Kate Kearney, Gonzaga University
- Daniel Heath, Pacific Lutheran University
- Christian Millichap, Linfield College

The Cascade Topology Seminar is supported in part by grants from the National Science Foundation and the Pacific Institute for the Mathematical Sciences. The support of these agencies is gratefully acknowledged. The Seminar has dedicated funding available to support the participation of graduate students, early career mathematicians, and members of traditionally underrepresented groups. Members of these aforementioned groups are especially encouraged to apply and attend.

### 26th NRW Topology Meeting

Meeting Type: conference

Contact: Martin Frankland

### Description

26th NRW Topology Meeting

November 25-26, 2016

University of Osnabrück

More information is available on the website.

### Workshop on W-algebras

Meeting Type: workshop

Contact: Peter McNamara, Arun Ram, Oded Yacobi

### Description

Overview: Our goal is to bring together postgraduate students, postdoctoral researchers, and faculty to participate in a week-long intensive exploration of W-algebras and related geometric and representation theoretic topics.

The workshop will be led by Tomoyuki Arakawa and Anne Moreau, renown experts in this area. The format is roughly "Talbot Style". This means that the mentors and organisers will design a series of 15-20 lectures. Several of these lectures will be given by the mentors and other experts in attendance, but the majority of talks will be given by the participants. There will also be problem sessions and time for casual discussion among the participants.

Agenda:

```
Day 1: Overview of theory and the goals of the workshop. Introduction to affine Lie algebras, and their representations.
Day 2: Vertex algebras and Zhu functors, Zhu's C2 algebra and the canonical filtration.
Days 3/4: BRST cohomology, quantum Hamiltonian reduction, finite and affine W-algebras
Days 4/5: Current topics such as rationality of W-algebras, the geometry of jet schemes, and chiral differential operators on groups.
```

A syllabus with bibliography will be posted here soon.

Funding: There will be limited funding available for travel and accommodations for participants; the amount of funding will depend on how many people register. We do not expect to be able to fund travel for participants from outside Australia.

Registration: Send an email to Oded Yacobi (oded.yacobi@sydney.edu.au) by July 30 with the following information

```
Name
University affiliation and status (postgraduate student, postdoc, etc...)
Research Interests and any other comments you may have. In particular let us know if you are requesting funding, and specifically how much you require.
```

The workshop aims to gather participants from wide background and all graduate educational levels, so applicants need not be experts in the field. We are also committed to promoting diversity in mathematics, so we especially encourage women and minorities to apply.

## December 2016

### 4th Metro Area Differential Geometry Seminar (MADGUYS)

Meeting Type: conference

Contact: see conference website

### Description

4th Metro Area Differential Geometry Seminar (MADGUYS), organized jointly by Howard University, Johns Hopkins University and the University of Maryland.

Speakers:

Sun-Yung Alice Chang (Princeton) Jake Solomon (Hebrew/IAS) Steve Zelditch (Northwestern)

All are invited, there are no registration fees. Young mathematicians and students are especially encouraged to attend.

Yanir Rubinstein

### Minischool on nonlinear equations and their applications

Meeting Type: Minischool

Contact: see conference website

### Description

The Harvard Math Department and the Center of Mathematical Sciences and Applications will host a minischool on nonlinear equations and their applications the weekend of December 3-4, 2016. The minischool will focus on major advances in the field of nonlinear PDEs and their applications in the last 30 years, and is aimed at graduate students and young researchers in PDE, geometry, mathematical physics and adjacent fields.

Confirmed speakers are:

Clifford Taubes (Harvard)

Valentino Tosatti (Northwestern)

Pengfei Guan (McGill)

Further speakers to be confirmed. Funding is available to offset the travel expenses of graduate students and young researchers.

### Bordism, L-theory, and Real Algebraic K-theory

Meeting Type: Winter school

Contact: see conference website

### Description

The winter school will consist of 5 short lecture series on recent developments in L-theory and real algebraic K-theory. See the website for the list of main speakers. The deadline for registration is September 15, 2016.

### Global Langlands correspondence

Meeting Type: collaborative research conference

Contact: see conference website

### Description

This workshop, sponsored by AIM and the NSF, This workshop, sponsored by AIM and the NSF will be devoted to the study of V. Lafforgue's groundbreaking work on the automorphic implies Galois direction of the Langlands conjecture for reductive groups over global function fields.

The primary goals will be:

```
To give a detailed exposition of the proof of V. Lafforgue's theorem.
Present related developments such as the Yun-Zhang proof of the Gross-Zagier type formula for function fields, the Genestier-Lafforgue construction for the local Langlands correspondence, and the connections with Fargues-Fontaine curve.
Discuss potential further developments that the ideas from V. Lafforgue's work lead us to.
```

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

### Workshop on Combinatorial Moduli Spaces and Intersection Theory

Meeting Type: conference

Contact: Dan Abramovich, Izzet Coskun, Angela Gibney, Gregory G. Smith, and Mike Stillman

### Description

Part of the Thematic Program on Combinatorial Algebraic Geometry. Please register on the Fields Institute website http://www.fields.utoronto.ca/cgi-bin/register?form_selection=CAG2016

### Masterclass "Hilbert Scheme and random walks"

Meeting Type: masterclass

Contact: etienne Mann

### Description

Masterclass "algebraic geometry and probability"

Angers, LAREMA, from 13rd to 15th December http://www.lebesgue.fr/content/seminars-masterclass

Master 2 students, PhD students or interested researchers are very welcome. The registration can be done online http://www.lebesgue.fr/content/seminars-masterclass-registration_support

Lectures will be in the morning sessions and exercises sessions will take place in the afternoon. We will have two parallel sessions:

Laurent Evain : The Hilbert scheme. The programm is grassmannian varieties, Hilbert scheme and some applications.

Rodolphe Garbit: Counting paths in an orthant: a probabilistic approach The lectures will be on the brownian motion, random walks and its applications in some combinatoric problems.

We will pay the housing with the breakfasts. The other meals are not payed by the organizers. For the travel expenses, we will do our best in the limit of our budget.

### The 4th Israeli Algebra and Number Theory Day

Meeting Type: conference

Contact: Lior Bary-Soroker, Mark Shusterman

### Description

Organizers: Lior Bary-Soroker and Mark Shusterman

Speakers: Will Sawin (ETH Zurich), Igor Rivin (Univeristy of St Andrews), Zeev Rudnick (Tel Aviv University)

## 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.

### Hypergeometric motives and Calabi-Yau differential equations

Meeting Type: conference

Contact: see conference website

### Description

- week 1: Hypergeometric motives and finite hypergeometric functions.
- week 2: Both topics.
- week 3: Arithmetic and combinatorial properties of periods of Calabi–Yau manifolds: differential equations satisfied by them, modularity, applications in mirror symmetry, random walks and other areas.

### Atelier PARI/GP

Meeting Type: software development workshop

Contact: see conference website

### Description

This workshop is organized to discuss the current and future development of the PARI/GP system. Anyone interested in helping out is welcome !

The workshop will include

(1) Short status reports on the current development projects.

(2) Tutorial sessions.

(3) Brainstorming sessions, to spell out and discuss ideas about the system development: new features, new algorithms, improving old implementations, bug fixes, extensions to GP syntax, documentation overhaul ...

(4) Coding sessions: inspired by (3), but bring also your own problems !

Please share your ideas for Discussion topics (3) or Coding sessions (4) with the development mailing list pari-dev@pari.math.u-bordeaux.fr. Feel free to suggest subjects for the Tutorial sessions (2).

### QUANTMOD-Quantization and Moduli Spaces

Meeting Type: conference

Contact: see conference website

### Description

The purpose of this workshop is to bring together mathematicians working in the field of moduli spaces of geometric and algebraic structures which might be related to mathematical aspects of quantization.

Confirmed speakers include:

Jorgen Andersen Philip Boalch Vladimir Fock Jochen Heinloth Lotte Hollands Motohico Mulase Christian Pauly Du Pei Nicolai Reshetikhin Pavel Safronov Armen Sergeev Oleg Sheinman Jörg Teschner Richard Wentworth

The organizers:

Jorgen Andersen (Aarhus University) Ozgur Ceyhan (Luxembourg) Francois Petit (Luxembourg) Martin Schlichenmaier (Luxembourg)

### The AIMS-Stellenbosch Number Theory Conference 2017

Meeting Type: Conference

Contact: Florian Breuer, Barry Green, Patrick Rabarison

### Description

This international conference will be hosted at the Department of Mathematical Sciences of the University of Stellenbosch, as well as at the African Institute for Mathematical Sciences, South Africa and the goal of this conference is to give a broad perspective of areas of modern number theory and to highlight some recent advances. This conference is one of the biennial Number Theory meetings which has been held at Stellenbosch University since 1997.

### 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.

### Algebraic Geometry and Complex Geometry

Meeting Type: conference

Contact: see conference website

### Description

The aim of this conference is to get together algebraic geometers and complex geometers, around recent topics of interest. Participants are mostly researchers from european universities but everybody is welcome to participate (please note that the number of participants is limited).

It is organised by the GDR 3064 Geometrie Algebrique et Geometrie Complexe (Research Group of the CNRS, French Scienti c Reseach Comity).

Mornings are devoted to 5 mini-courses, given by experts of important new developpments.

Topics covered are :

- Dynamical degree of birational transformations of surfaces, given by Jérémy Blanc (Universität Basel, Suisse).
- Gromov-Witten invariants, Mirror symmetry and degenerations of Calabi-Yau's, given by Mark Gross (University of Cambridge, Angleterre).
- Berkovich spaces, degenerations of algebraic varieties, skeleton, given by Johannes Nicaise (University of Leuven, Belgique).
- Stable rationality, given by Alena Pirutka (Ecole Polytechnique).

The afternoons are devoted to more specialized 50 minutes talks. They will be chosen by the scientific committee 3 months before the conference. A short talks (10 minutes) session will be also organized during the conference to enable participants to talk about their works or some open questions.

### Number Theory

Meeting Type: research program, conference

Contact: see conference website

### Description

The goals of this program are to promote high-quality research in Number Theory in Barcelona, as well as to contribute to the training of researchers in this and related areas. It will combine research conferences, courses, and instructional workshops. In particular, it will bring together worldwide experts in the field with the aim to foster advances in the research projects of the involved BGSMath members and groups. Namely we plan to focus on the following ground-breaking lines of research:

Euler systems and the conjectures of Birch and Swinnerton-Dyer and Bloch-Kato. In order to celebrate mathematics in the new millennium, the Clay Mathematics Institute established seven $ 1.000.000 Prize Problems. The Prizes were conceived to record some of the most important challenges with which mathematicians were grappling at the turn of the second millennium. One of these is the conjecture of Birch and Swinnerton-Dyer (BSD), widely open since the 1960’s, together with other cornerstones in mathematics like the Riemann hypothesis, Hodge conjecture, P vs NP problem, Navier-Stokes equation, Yang-Mills and Mass gap, and the Poincare conjecture. The Birch and Swinnerton-Dyer conjecture stands as the tip of the iceberg formed by the vast conjectural program of Beilinson, Bloch and Kato, and all the attempts taken so far to proving it exploit the deep connections between Shimura varieties, Galois representations and automorphic forms. Hence the conjecture can actually be stated in a much more general context, including the twist of E by irreducible Artin Galois representations of the absolute Galois group GK of K. The generalization of BSD formulated by Bloch and Kato applies to arbitrary motives arising from higher-dimensional varieties.

Experience shows that it might be more natural and fruitful to stare at the conjecture from this broader perspective, and this becomes apparent in this project, where the full picture is exploited in order to derive a neat strategy for proving new instances of the original BSD and solving important related problems.

During the research program hosted by the BGSmath we plan to develop innovative and unconventional strategies for proving groundbreaking results towards the resolution of the conjecture of Birch and Swinnerton-Dyer on elliptic curves over number fields and their generalizations by Bloch and Kato (BK) to arbitrary motives associated to higher-dimensional algebraic varieties over global fields. Moreover, we hope to exploit our background and experience on this subject in order to apply our methods and techniques for establishing bridges with our areas and prove important results concerning related questions.

Arithmetic Langlands Program: advances in reciprocity and functoriality. The Langlands Program is considered to be one of cornerstones of modern arithmetic geometry. It predicts a precise relation between automorphic forms on the one hand and arithmetic varieties and their Galois representations on the other. Particular cases of this relationship are the celebrated Shimura-Taniyama-Weil conjecture, proved by Wiles and Taylor-Wiles as the key step in their proof of Fermat’s Last Theorem, and Serre’s Modularity Conjecture, now a theorem thanks to the groundbreaking works of Khare, Wintenberger, and Dieulefait.

During the six-weeks program we plan to achieve fundamental results linking automorphic forms and Galois representations, with special emphasis on Langlands functoriality results, base change and modularity over totally real number fields.

## February 2017

### Connections for Women: Analytic Number Theory

Meeting Type: conference

Contact: see conference website

### Description

This workshop will consist of lectures on the current state of research in analytic number theory, given by prominent women and men in the field. The workshop is open to all graduate students, post-docs, and researchers in areas related to the program; it will also include a panel discussion session among female researchers on career issues, as well as other social events

### Introductory Workshop: Analytic Number Theory

Meeting Type: conference

Contact: see conference website

### Description

The introductory workshop will present, through short minicourses and introductory lectures, the main topics that will be the subject of much of the Analytic Number Theory Programme at MSRI. These topics include the theory of multiplicative functions, the theory of modular forms and L-functions, the circle method, sieve methods, and the theory of exponential sums over finite fields

### Young researchers in homotopy theory and categorical structures

Meeting Type: conference

Contact: Viktoriya Ozornova, Claudia Scheimbauer

### Description

The aim of this mini-conference is to bring together young researchers working in the field of homotopy theory and/or categorical structures. It should provide an opportunity for exchange of ideas, presentation of ongoing research, and interaction with experts. In addition to seven invited talks, there will also be several contributed talks. Furthermore, there will be a series of very short talks, aka "gong show". We encourage early career-stage participants to submit a tentative abstract for a contributed and/or for a very short talk.

Limited financial support is available. The deadline for financial support is December 15, 2016. For more information, please see the conference webpage.

Invited Speakers: Dimitri Ara, Moritz Groth, Rune Haugseng, Kathryn Hess, Ieke Moerdijk, Angélica Osorno, Martina Rovelli.

### p-adic Methods for Galois Representations and Automorphic Forms

Meeting Type: conference

Contact: see conference website

### Description

The conference aims to bring together researchers to present their work and recent developments in the field. The goal is also to provide a fruitful atmosphere to encourage discussions and to foster new collaborations among the participants. The event is part of the Monthly Program on Number Theory of the BGSMath.

## March 2017

### The Georgia Algebraic Geometry Symposium

Meeting Type: conference

Contact: see conference website

### Description

The Georgia Algebraic Geometry Symposium is a conference series, jointly organized by the University of Georgia, Emory University and Georgia Tech.

### Arizona Winter School: Perfectoid Spaces

Meeting Type: school

Contact: Bryden Cais, Kiran S. Kedlaya

### Description

### New Trends in Arithmetic and Geometry of Algebraic Surfaces

Meeting Type: conference

Contact: see conference website

### Description

The interplay of arithmetic and geometry has been a driving force in the study of algebraic curves, culminating in Faltings' finiteness theorem for rational points on curves of general type. For algebraic surfaces, such deep structures are mostly still conjectural, but great progress has been made in recent years following this leitmotif. The most spectacular achievement of the last few years might have been the proof of the Tate conjecture for K3 surfaces due to Madapusi, Maulik and Charles. However, this is only the brightest star among a plentitude of amazing results manifesting the intertwining of arithmetic and geometry (and also initiating new directions, for instance in dynamics). In the following, we shall highlight a few streams of research which we consider of utmost relevance for our workshop.

K3 surfaces are the most prominent player in our story, notably because of their versatility and also because of their relevance to neighboring areas such as differential geometry and physics. Beyond the breakthrough on the Tate conjecture, there have several further important developments on K3 surfaces in the last few years:

- Good reduction and Honda-Tate (Matsumoto, Liedtke, Taelman);
- unirationality (Liedtke, Lieblich);
- moduli of K3 surfaces, in particular relating to double sextics, elliptic K3 surfaces and degenerations of K3 surfaces and their relation with arithmetic (Alexeev, Brunyate, Elkies, Hacking, Kumar, Laza, Thompson);
- dynamics (Blanc, Cantat, Esnault, McMullen, Oguiso, Sch\"utt).

We would also like to emphasize the experimental approach towards arithmetic and geometry of K3 surfaces (closely related to the developments sketched above). As an illustration, consider the important problem how the Picard number of a K3 surface X defined over some number field behaves under reduction. By work of Li and Liedtke, this has important implications for rational curves on X, since an infinitude of places with the Picard number increasing upon reduction can be used to produce an infinitude of rational curves on the original surface. For odd Picard number, this crucial reduction property follows from the Tate conjecture, but for even Picard number, it seems only to be known in special cases such as Kummer surfaces of product type (Charles). This is where experiments using zeta functions (Elsenhans, Jahnel) and p-adic cohomology (Costa, Harvey) enter. We expect that this area of ideas might see important progress until 2017.

Enriques surfaces are closely related to K3 surfaces, yet they come with intriguing subtleties which have been a driving force for the investigation of the deep structures of algebraic surfaces. Historically, they have been among the first surfaces (together with Godeaux surfaces) which were shown to be non-rational despite sharing the Q -cohomology with the projective plane blown up in a finite number of points (which thus led Castelnuovo to formulate his rationality criterion in terms of the second plurigenus). From today's perspective, this special role of Enriques surfaces manifests itself prototypically in the study of finite group actions. For instance, there are complex Enriques surfaces with finite groups of automorphisms acting trivially on cohomology (with Q or even Z

coefficients). In a similar direction, Enriques surfaces with finite automorphism group are very special; both properties are completely contrary to what happens for K3 surfaces. We would like to highlight the following recent projects (partly ongoing):

- Semi-symplectic finite group actions on Enriques surfaces and their relation to the Mathieu group M12
- Moduli of polarized complex Enriques surfaces (Gritsenko, Hulek)
- Enriques surfaces in characteristic 2 (Katsura, Kondo, Liedtke, Shepherd-Barron)

Surfaces of general type form the most mysterious class of algebraic surfaces. There are still many open problems about them, such as the classification of surfaces of general type and their moduli spaces, and often rather surprising results! We anticipate that the workshop will feature lectures on algebraic surfaces of general type, but from today's perspective it is not so clear in which direction research on surfaces of general type will head in the next years. Therefore, next to above classical topic, we only emphasize the central role that derived categories have lately played for surfaces of general type, in particular for Godeaux surfaces, Burniat surfaces and Barlow surfaces. Notably, there have been deep results on exceptional collections and phantom categories (Alexeev, B\"ohning, Katzarkov, Orlov, Sosna).

For the precise conference program, we will also take into account the latest developments that might succeed this proposal, thus giving an up-to-date account of the arithmetic and geometry of algebraic surfaces.

The conference is meant to foster the interactions between experts working on algebraic surfaces. The inspiring atmosphere of the BIRS will allow them to share their ideas and latest results, and hopefully it will initiate new collaborations and programs. At the same time, we hope to attract many junior participants from Canada and the United States and abroad and give them the opportunity to gain insight into the latest developments in algebraic and arithmetic geometry and learn about new methods directly from the inventors.

In particular we hope to attract many female participants. Among some 75 potential participants as listed below, we are targeting 19 female researchers at all career stages. Thus we are optimistic to have the community of women working on the topic of the conference represented very well at BIRS.

### Homological Mirror Symmetry: Emerging developments and applications

Meeting Type: workshop

Contact: see conference website

### Description

This is one of two workshops during a year-long program.

During the 2016-17 academic year, the School will have a special program on Homological Mirror Symmetry. Paul Seidel, from MIT, will be the Distinguished Visiting Professor. Maxim Kontsevich, from IHES, will be attending the program for one month during each of the fall and spring terms (from mid-October to mid-November, and for the month of February). Denis Auroux, from UC Berkeley, will be attending for the spring term.

### Theta constants, Schottky relations, and local zeta functions: 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 survey recent developments inspired and influenced by the work of Jun-Ichi Igusa.

### 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

### 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.

### Flows and Limits in Kähler Geometry

Meeting Type: school

Contact: see conference website

### Description

Organization board: Sébastien Boucksom, Yann Rollin, Carl Tipler

Scientific board: Claudio Arezzo, Olivier Biquard, Paul Gauduchon, Michael Singer

Kähler geometry is a very active research field, at the crossroads between algebraic and Riemannian geometry. Important breakthrough, that lead to solve the Yau-Tian-Donaldson conjecture in the Fano case, have been achieved recently. A spring school involving mini-lectures and talks around this thread of new ideas in Kähler geometry is organized at Nantes University. The goal of the school is to develop certain technical skills, useful to address a variety of important questions in algebraic geometry and global analysis on manifolds, aimed for PhD students and young researchers. Geometric flows, like the Kähler-Ricci flow for instance, and the associated quantification by the Donaldson dynamical system, will be among the essential tools dealt with during the school.

### 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

### 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)

### 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

### 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.

### 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.

### Low-Dimensional Topology and Geometry

Meeting Type: conference

Contact: Spencer Dowdall

### Description

### 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

### 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.

### 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

### Mathematics Research Communities: Homotopy Type Theory

Meeting Type: MRC workshop

Contact: Chris Kapulkin

### Description

### 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.

### 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.

### 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.

## 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

### 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

### 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.

## 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: conference

Contact: see conference website

### Description

The first Women in Numbers workshop was held at BIRS in 2008, with the explicit goals of highlighting the research of female number theorists and increasing the participation of women in number theory research. In their original proposal, the organizers cited the lack of representation of women in major institutions and at major international conferences.

Since that first proposal, 84 different women have participated in three WIN conferences at BIRS, with an additional 40 participants at the Women in Numbers -- Europe conference held at CIRM in Luminy. The number of female number theorists is steadily growing. The visibility of the WIN conferences --- due both to the community that has developed and the high quality of research output from these workshops --- has helped to raise awareness in the broader community of the important contributions made by these researchers. In the years since the first WIN conference, there has been a steady trend of increasing representation at these major conferences as shown in Table~???

.

\begin{table}[b] \begin{tabular}{l|c||cc}

Algebraische Zahlentheorie & 2005: 1/19 & 2011: 3/19 & 2014: 5/19 \ Algorithmic Number Theory Symposium & 2006: 4/39 & 2012: 5/25 & 2014: 4/31 \ Canadian Number Theory Association (plenary)& 2006: 0/15 & 2012: 1/10 & 2014: 2/10 \ Explicit Methods in Number Theory & 2005: 1/30 & 2013: 4/24 & 2015: 4/15 \ Journ\'ees Arithm\'etiques & 2007: 0/12 & 2015: 3/12&\ \end{tabular}\caption{Number of female speakers in past number theory conferences}\label{table:NumSpeakers} \end{table}

It is difficult to know exactly how much of this increase is due (directly or indirectly) to WIN. It is certainly worth noting that many of the invited speakers at these conferences were participants in one or more of the WIN conferences. Even more importantly, WIN alumnae are encouraged to organize their own conferences and to participate in scientific boards for major conferences. It has been well-documented that when women are included as conference organizers, more women are invited as speakers and participants (see, for instance, the statistics collected by the AMS).

Many participants told us that the previous WIN conferences ignited their careers. For the graduate students, it was eye-opening to see the level of intensity of the projects. Junior faculty, both postdocs and assistant professors, seemed to gain the most from the WIN experience. Several mentioned that the WIN projects introduced them to completely new directions for research. Faculty with high teaching loads appreciated the chance to focus on research. For group leaders, it was a formative experience to find new research problems and direct a research group.

In addition, many women who attended the first WIN conference as graduate students and postdocs (including three of the four organizers of the proposed workshop) have gone on to tenure track positions at major research universities, including University of California at San Diego, University of Colorado at Boulder, University of Hawaii at Manoa, University of Lethbridge, University of Oregon, and University of Washington. Several who participated as postdocs or assistant professors now hold tenured positions.

Another major indicator of the success of the WIN conferences is the publication output: three proceedings volumes containing a total of 36 papers (including some survey papers), as well as more than 10 journal articles published elsewhere. This far surpasses the output of a typical research workshop or graduate focused workshop such as Arizona Winter School.

Less tangible but equally important outcomes include the lasting bonds formed between beginning researchers and their mentors, and the invigorating effect of the conferences on this mathematical community. WIN created a new model of working research conference designed to build networks of female researchers. Inspired by the success of WIN conferences, women in other fields have organized similar conferences at math institutes over the past few years, each focused on building collaboration groups consisting of senior and junior women in a given area. These include: Algebraic Combinatorixx and Women in Topology (WIT) at BIRS; Women in Shape (WiSh) at IPAM; and two Women in Applied Math conferences at IMA, Dynamical Systems with Applications to Biology and Medicine (WhAM!) and Numerical PDEs and Scientific Computing (WhAM2!). Each of these conferences has resulted in new, high-quality mathematics research as well as lasting collaborations among attendees.

These are positive changes, but our work is not done. Visibility of women at international number theory workshops and conferences, though increasing, continues to be low, with percentages of female speakers rarely exceeding 20\%. Women are still underrepresented in major research universities, especially at the most prestigious institutions. Women researchers receive disproportionately less grant money from the NSF than their male peers. It is imperative that we continue to build on the success of the WIN and other research collaboration conferences for women, creating supportive networks for women at the early stage of their careers.

In recognition of these tremendous successes and the continued need, the National Science Foundation has recently awarded the AWM a $750,000 ADVANCE grant to spread and support the WIN model for women in research in mathematics to all fields of mathematics. This five-year grant will provide funding for supporting the network of research collaboration conferences for women, including some funding for participant travel. Also, Springer has established the Association for Women in Mathematics series, focusing on the groundbreaking work of women in mathematics past, present, and future. The series already has nine planned titles, including Proceedings volumes for both the Women in Numbers 3 and the Women in Numbers -- Europe conferences.

The proposed workshop aims to continue this important work, promoting research and leadership among female number theorists within a supportive environment. The specific goals of the workshop are:

```
to generate research in significant topics in number theory;
to broaden the research programs of female number theorists, especially pre-tenure;
to train female graduate students and postdocs in number theory, by providing experience with collaborative research and the publication process;
to strengthen and extend a research network of potential collaborators in number theory and related fields;
to enable female faculty at small colleges to participate actively in research activities including mentoring graduate students and postdocs; and
to highlight research activities of women in number theory.
```

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. Each group will have one or two leaders chosen for their skill in both research and communication. Prior to the conference, these leaders will design projects and provide background reading and references for their groups. At the conference, there will be some talks, but ample time will be dedicated to working groups, particularly in the afternoons and evenings. 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.

The scientific themes of the workshop will include Apollonian circle packings, arithmetic dynamics, arithmetic statistics, and nonarchimedean tools. The broad scope of the WIN conferences encourages the leaders to find connections between their topics. For example, at WIN2, unexpected synergy emerged between several groups focused on surfaces (reduction of abelian surfaces, modular forms on K3 surfaces, zeta functions of surfaces, etc).

We have already identified potential project leaders (listed below) for each of these exciting topics. Several (but not all) of these researchers have participated in past WIN conferences. An asterisk (*) indicates demonstrated interest in attending WIN4 and leading a project.

```
Apollonian circle packings.} {\it Potential leaders: Elena Fuchs*, Hee Oh, and Katherine Stange*.
Apollonian circle packings arise from the seemingly simple process of iteratively filling in the gaps between triples of mutually tangent circles with pairs of circles tangent to all three of them. The study of these designs dates back at least to Apollonius, circa 200 BC. A series of articles by Graham et al. in 2005--2006 explored surprisingly deep and interesting group theoretic and number theoretic connections to this classical geometric construction and set off a surge of recent activity in the area, including the 2014 European Women in Mathematics summer school.
Arithmetic dynamics:} {\it Potential leaders: Holly Krieger* and Michelle Manes*.
Arithmetic dynamics is concerned with the behavior of the forward orbit of a point under ϕ:X→X
```

a morphism of an algebraic variety X. In the early 1990s, Call and Silverman introduced the canonical height of a dynamical system as an analog of the N\'{e}ron-Tate canonical height on an abelian variety. Like N\'{e}ron-Tate heights, h^ϕ is nonnegative-valued, and zero only at points with finite forward orbit, the dynamical analogs of torsion points. Together with work of Morton and of Morton and Silverman on dynamics over number fields, the introduction of canonical heights breathed new life into a subject that had lay all-but-dormant since the 1940s. This foundation paved the way for an ongoing flurry of activity in the 2000s and 2010s, and the subject has proven to be a rich one, generating numerous deep questions, examples of fascinating phenomena, and powerful machinery.

Arithmetic statistics:} {\it Potential leaders: Chantal David* and Melanie Matchett Wood*. The burgeoning field of arithmetic statistics lies at the intersection of arithmetic algebraic geometry, automorphic forms and representation theory, analytic number theory, and statistics, including statistical heuristics obtained from the contemporary work regarding random matrices. Recent growth in our understanding of the analytic properties of L-functions has led to profound applications regarding statistics related to arithmetic problems, including Bhargava and others' bounds on the average rank of elliptic curves. This field is the center of much excitement in number theoretic research, and has been the focus of a 2011 semester-long program at MSRI, a 2012 MRC workshop, and the 2014 Arizona Winter School.

Nonarchimedean tools:} {\it Potential leaders: Jennifer Balakrishnan* and Julia Gordon*. Nonarchimedean tools --- in particular, methods from p-adic analysis and geometry --- have inspired a number of beautiful results in recent years. Coleman used p-adic integration to re-interpret the method of Chabauty to find rational points on curves, and variations of this technique have been used to produce results in the arithmetic statistics of higher genus curves. The program of Kim aims to give a nonabelian analogue of the Chabauty-Coleman method on the way to an explicit Faltings' theorem on finiteness of rational points. Scholze's work on perfectoid spaces has revolutionized p-adic geometry, leading to a number of striking results in just the last few years in p

```
-adic Hodge theory and the Langlands program.
```

Current and past organizers may also lead projects: Matilde Lal\'in (Mahler measure), Kristin Lauter* (abelian varieties, cryptography), Rachel Pries* (algebraic curves, abelian varieties), and Renate Scheidler (class groups).

We aim to make a few improvements based on participant feedback from the previous WIN conferences. We have found that the research collaboration conferences have the greatest impact on the careers of postdocs and young faculty, who have already built sufficient mathematics background to get up and running on a project quickly and are often looking for new research directions. Therefore, we will include more participants at this career level. We will accept fewer graduate students, being more selective in the background requirements for the research projects to ensure that the graduate students who do attend can be fully integrated into their research group. We will also make a more concerted effort to include faculty from teaching-oriented colleges. We have also heard from some project leaders that while they enjoy mentoring young mathematicians, they would like part of the conference to be more directly beneficial to them, providing an opportunity to build or continue research collaborations with other more senior participants. We expect that the new makeup of the participant pool will mean that several of the project groups will work more independently from their group leaders than in the past. In this case, the group leaders will have significant time to work together exploring areas of mutual interest. This is especially desirable for group leaders who are still early- or mid-career and need to balance new leadership roles with their own research progress.

### 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

### 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

### 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

### 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.

## 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.

[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).

### 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.

## July 2018

### 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.

## 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.