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## Or choose your own subject tags below

Welcome to MathMeetings.net! This is a list for research mathematics conferences, workshops, summer schools, etc. Anyone at all is welcome to add announcements.

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

#### Updates 2017-10

- Secure connections (https) now activated and all traffic is automatically redirected to use https. Thanks to Let's Encrypt for providing the certificate!
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- New json and xml interfaces for access by other software.

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

# Upcoming Meetings

## 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.

## January 2018

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

Meeting Type: conference

Contact: see conference website

### Description

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

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

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

### Model theory, combinatorics and valued fields

Meeting Type: thematic program

Contact: see conference website

### Description

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

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

The programme will bring together researchers on the following topics:

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

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

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

## March 2018

### The Homological Conjectures: Resolved!

Meeting Type: conference

Contact: see conference website

### Description

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

### 32nd Automorphic Forms Workshop

Meeting Type: conference

Contact: see conference website

### Description

ver the last 30 years, the Annual Workshop on Automorphic Forms and Related Topics has remained a small and friendly conference. Those attending range from students to new PhD's to established researchers. For young researchers, the conference has provided support and encouragement. For accomplished researchers, it has provided the opportunity to mentor as well as a forum for exchanging ideas.

The workshop has become internationally recognized for both its high-quality research talks and its supportive atmosphere for junior researchers. Participants present cutting-edge research in all areas related to automorphic forms. These include mock modular forms, Maass wave forms, elliptic curves, Siegel and Jacobi modular forms, special values of L-functions, random matrices, quadratic forms, applications of modular forms, and many other topics.

In addition to research talks, the workshop has, in the past years, featured panel discussion sessions on the topics of grant writing, mentoring and research partnerships, REUs and outreach, and opportunities for international collaborations. Based on the success of these sessions, we have similar panel sessions this year as well.

This year, the 2018 Automorphic Forms Workshop will be held in Medford, Massachusetts at Tufts University. The workshop is being organized by faculty at Tufts University, Amherst College, and Williams College.

### Picard-Fuchs Equations and Hypergeometric Motives

Meeting Type: conference

Contact: see conference website

### Description

### A Day of Algebraic Geometry in Savannah

Meeting Type: Mini Conference

Contact: Jimmy Dillies

### Description

We will hold

"A Day of Algebraic Geometry in Savannah"

workshop which will take place at the Armstrong Campus of Georgia Southern University in Savannah, GA, March 31st 2018.

List of speakers: Valery Alexeev (UGA) Matthew Ballard (USC) Ana-Maria Castravet (Northeastern) Angela Gibney [*] (Rutgers) Emanuele Macrì (Northeastern)

For more information on the meeting and registration, please check the website

http://jimmy.klacto.net/DAGS/

Hoping to see you in Savannah, Jim Brawner Sungkon Chan Jimmy Dillies Davide Fusi (USC) Enka Lakuriqi

[*] to be confirmed

## April 2018

### Arbeitsgemeinschaft: Topological Cyclic Homology

Meeting Type: learning workshop

Contact: see conference website

### Description

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.

### Crystals and Geometry in Characteristic p

Meeting Type: conference

Contact: Oli Gregory, Roberto Laface, Christian Liedtke, Gebhard Martin

### Description

The aim of this workshop is to bring together experts from different communities in the fields of algebraic and arithmetic geometry:

◾those with a more classical and geometric background, who work on moduli spaces, birational geometry, and the classification of higher dimensional objects, as well as

◾those with a more arithmetic background or those, who work on the foundations of crystalline cohomology, the de Rham-Witt complex, and general theories of period spaces and period maps.

To make this conference more easily accessible also for younger researchers (e.g. Ph.D. students and early PostDocs) and non-experts, Luc Illusie’s lecture series will introduce the de Rham-Witt complex and its applications to algebraic and arithmetic geometry.

### Spring Lecture Series: Old and New themes in p-adic Cohomology

Meeting Type: conference

Contact: see conference website

### Description

### Arithmetic of algebraic curves

Meeting Type: conference

Contact: see conference website

### Description

This is a workshop on arithmetic geometry, a hybrid of number theory and algebraic geometry. The goals of this conference include providing graduate students opportunities to give talks, increasing interaction between number theory and algebraic geometry research groups, and strengthening networks for mathematicians from underrepresented groups.

### Southern California Algebraic Geometry seminar

Meeting Type: conference

Contact: Aravind Asok, Dragos Oprea, Burt Totaro

### Description

Southern California Algebraic Geometry Seminar - Spring 2018
Where: University of Southern California, Kaprielien Hall 414
When: Saturday, April 14, 2018; Registration 9am, Talks begin at 10am

Speakers: Ben Antieau (UIC), Barbara Fantechi (SISSA), Tomasso de Fernex (Utah), Hiraku Nakajima (RIMS)

### Tropical geometry and amoebas in higher dimension

Meeting Type: conference

Contact: see conference website

### Description

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

Meeting Type: conference

Contact: Valerio Talamanca

### Description

### Algebraic Groups and Geometrization of the Langlands Program

Meeting Type: thematic program

Contact: see conference website

### Description

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

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

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

### Upstate New York Number Theory Conference

Meeting Type: conference

Contact: Joseph Hundley, James Ricci

### Description

A primary goal of the Upstate Number Theory Conference is to bring together the specialists from the various branches of Number Theory in the Upstate New York region and surrounding areas, and to expose the younger researchers to new and old problems in the field.

## May 2018

### Strength in Numbers

Meeting Type: Graduate Workshop

Contact: Please see the website

### Description

Strength in Numbers is a two-day workshop focusing on number theory and related areas, aimed primarily at graduate students. We especially encourage applications from underrepresented groups.

Each morning session will begin with two lectures by senior speakers, which will be accessible to graduate students in early years. Junior participants are invited to give short talks, on a topic of their choice.
A **novel feature** of this workshop is a presentation by Professor Erin Maloney, a psychologist specializing in math education, math research and surrounding problems. Math anxiety, stereotype threat and impostor syndrome are just a few of these issues. The presentation will be followed by a panel on professional development, led by the invited speakers. The participants are encouraged to ask questions, share their experiences and seek advice during this session. Registered participants will be given the opportunity to submit their questions aimed at the panel members, ahead of time, via an online form with the option of anonymous submissions.

### Birational Geometry and Arithmetic

Meeting Type: conference

Contact: Sho Tanimoto

### Description

### Iwasawa Theory and Related Topics

Meeting Type: conference

Contact: see conference website

### Description

### Motivic Homotopy Theory and Refined Enumerative Geometry

Meeting Type: Workshop

Contact: Federico Binda, Manh Toan Nguyen

### Description

The workshop will turn around three series of lectures on topics in motivic homotopy theory, with a particular emphasis on some recent applications in enumerative geometry.

The main goal of this workshop will be to provide a (detailed) introduction to some of the main tools and ingredients which go into the development of this theory.

The lectures are intended for graduate students, postdocs and young researchers. The sequence of lectures will be complemented by several research talks by experts in the field.

### Probability in Number Theory

Meeting Type: summer school, thematic program

Contact: see conference website

### Description

The appearance of Probability in Number Theory can be traced back to a famous collaboration of Erdős and Kac. Nowadays, probabilistic techniques are routinely used in the study of integers and L-functions. However, until recently there had not been much room for modern and deep techniques of probability theory. During the past few years this has changed notably. Conversely, number theoretic techniques and heuristics have been proven effective in resolving standing problems in combinatorics and discrete probability theory. The goal of this month-long program is to bring together experts from Number Theory and Probability to highlight and facilitate the interactions between these two fields of mathematics.

During the first week of our program, there will be a workshop (an ISM discovery school) aimed at young researchers (postdocs and advanced graduate students) who work or are interested in the field of Probabilistic Number Theory. The workshop will consist of mini-courses given by Kevin Ford (Illinois), Adam Harper (Warwick), K. Soundararajan (Stanford) and Terence Tao (UCLA).

The remainder of the program will gather at CRM several of the leading experts in the fields of Probability and Number Theory. We also invite applications for five month-long postdoctoral positions (details to follow). Among other things, we will run a frequent research seminar for the participants of our program.

### Chromatic Homotopy Theory: Journey to the Frontier

Meeting Type: conference and graduate student workshop

Contact: Agnes Beaudry, Markus Pflaum, Mike Hill, Dylan Wilson

### Description

This four day event centered around the topic of Chromatic Homotopy Theory will consist of a graduate student workshop on May 16-17 and research talks by prominent researchers in the field on May 18-20. Participants who are not part of the graduate student workshop are invited arrive on May 17 and take part in the second day of the workshop.

More information will be posted on our website soon.

### NSF-CBMS Conference on Additive Combinatorics from a Geometric Viewpoint

Meeting Type: instructional conference

Contact: see conference website

### Description

Additive combinatorics is a very active area of mathematics. It is the crossing point of number theory, harmonic analysis, ergodic theory, and combinatorics. Beyond the numerous conferences and workshops, special semester-long programs have been organized on the subject at Princeton (IAS), Cambridge (Newton Institute), UCLA (IPAM), and UC Berkeley (MSRI). In this series of lectures, Dr. Jozsef Solymosi (University of British Columbia) provides an elementary introduction to additive combinatorics using discrete geometry, algebra, extremal combinatorics, and a bit of algebraic geometry. He also shows how to apply these techniques in order to attack Erdos type problems in discrete geometry. The lectures and the monograph to be written are intended for graduate students and researchers working on related areas, and to help those who intend to enter the field.

Dr. Solymosi will give 10 lectures on the topic of the conference, which will be complemented by 4 one-hour lectures (by Gyula Karolyi, Giorgis Petridis, Orit Raz, and Joshua Zahl). Problems to be solved will be distributed and discussed. Open problem sessions will provide opportunity for collaboration among the participants. This program is designed for graduate students and early-career researchers. As seating is limited, prospective participants not affiliated with the University of South Carolina must submit an application before January 31, 2018 at: http://mathprograms.org/db/programs/622

The application must include a CV with date or expected date of Ph.D., an email address, a letter of reference, a statement of research interests, a publication list, and a statement on how participation is expected to enhance the applicants career.

Selection of participants will take place in the first two weeks of February. Acceptance letters will be sent out as soon as final selections have been made. Selection will focus on the background of the participants in relevant areas and the expected effect of the program on their career. In particular, we encourage young mathematicians from the Southeast and members of underrepresented groups in the mathematical sciences to apply. Approved applicants will be provided dorm accommodation and partial reimbursement of other expenses.

Arrival to the conference should be scheduled for May 20, 2018. The scientific program is scheduled for May 21-25, 2018.

### Diophantine geometry

Meeting Type: conference

Contact: Eric Gaudron;

### Description

### Midwest Algebraic Geometry Graduate Seminar

Meeting Type: conference

Contact: Jay Kopper, Yajnaseni Dutta, Sayanta Mandal, Sebastian Olano, Fumiaki Suzuki

### Description

Midwest algebraic geometry graduate conference will be held at UIC May 25-27. As this is a conference for graduate students, we welcome the submission of any abstracts for talks and/or posters on original graduate research in algebraic geometry. Limited funds are available for housing for registered participants. The deadline to register to be considered for funding or to submit an abstract is March 15, 2018.

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

Meeting Type: conference

Contact: see conference website

### Description

### Conference on Modular Forms and Related Topics

Meeting Type: conference

Contact: see conference website

### Description

Conference on modular forms and related topics has two objectives. The First is to introduce the local community to the recent significant developments in the theory of modular forms and related topics. The second objective is to encourage young Lebanese mathematicians to pursue their graduate studies in this area that has different applications in different mathematical sciences.

### Algebra, Arithmetic and Combinatorics of Differential and Difference Equations

Meeting Type: conference

Contact: see conference website

### Description

In recent years, there have been several important advances in the theory of differential and other functional equations. This field of research lies at the interface between several areas of mathematics, e.g., number theory, model theory, combinatorics and automata theory, theoretical physics, theoretical informatics, etc. This conference aims to gather researchers from a variety of backgrounds, whose research is related to the theory of functional equations. We will address theoretical as well as effective aspects. This is an international conference, every interested researcher can apply.

La théorie des équations différentielles et autres équations fonctionnelles a connu d’importantes avancées ces dernières années. Elle se situe à l’interface de nombreux domaines des mathématiques, dont la théorie des nombres, la théorie des modèles, la combinatoire et la théorie des automates, la physique théorique, l’informatique théorique, etc. L’objectif de cette rencontre est de favoriser les interactions entre mathématiciens issus d’horizons variés et dont les recherches touchent aux équations fonctionnelles. Nous aborderons aussi bien les aspects théoriques qu’effectifs. Il s’agit d’une rencontre internationale, ouverte à toute personne souhaitant y participer.

### Shimura varieties and hyperbolicity of moduli spaces

Meeting Type: conference

Contact: see conference website

### Description

The purpose is to gather experts from two mathematical communities, arithmetic geometry and complex geometry, who study from different perspectives Shimura varieties and questions related to hyperbolicity of moduli spaces.

The geometry of quotients of bounded symmetric domains $\Omega/\Gamma$ has been the subject of many works. Classical results (Mumford, Tai, Tsuyumine, etc.) and more recent ones (Bakker-Tsimerman, Brunebarbe, Cadorel, etc.) state that in most cases compactifications of such quotients have many differential forms. In particular, they are of general type. The geometry of entire curves has also been investigated (Nadel, Noguchi, Rousseau, etc.) showing that such quotients are in general hyperbolic modulo the boundary. Some recent works (Brunebarbe, Cadorel, etc.) have also established that all subvarieties of $\Omega/\Gamma$ are of general type. These results can be seen as illustrations in this context of the Green-Griffiths-Lang's conjectures which make a natural bridge with arithmetic problems.

Many conjectures on the arithmetic side indeed involve the study of subvarieties of Shimura varieties. There has been a lot of work around the so-called Andr\'e-Oort conjecture on special subvarieties of Shimura varieties (Klingler-Yafaev, Ullmo, Pila, Tsimerman, etc.) which was recently proved for $\mathcal{A}_g$, the moduli space of abelian varieties of dimension $g$, by J. Tsimerman by relying in particular on the so-called Colmez conjecture in average proved by Andreatta-Goren-Howard-Pera. There is on-going work using a similar line of attack that was successful to prove Andr\'e-Oort to investigate its generalization, labelled the Zilber-Pink conjecture for brevity, for example by Daw and Ren in the direction of the hyperbolic Ax-Schanuel conjecture. The interplay between complex geometry and arithmetic geometry relies on direct applications to Shimura varieties of general theorems from complex geometry; on the suggestive analogy between the complex category and the arithmetic setting; but also on more intertwined interactions.

### Connecticut Summer School in Number Theory

Meeting Type: summer school, conference

Contact: see conference website

### Description

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. The summer school will expose undergraduate and graduate students to important ideas in number theory. The research conference following the school is open to participants of all levels, including senior and junior faculty, and interested students. In particular, summer school students’ participation in the research conference will allow them hear about recent developments in the areas of elliptic curves, modular forms, and related topics.

This is a seven-day event, consisting of a four-and-a-half-day summer school followed by a two-and-a-half-day conference, from Monday, May 28th to Sunday, June 3rd, 2018, at the University of Connecticut at Storrs. The conference will feature research talks on number theory.

During the day, the summer school will have lectures aimed at undergraduate and graduate students. In the evenings, students will work in groups on problem sets and projects, both computational and theoretical in nature. The conference to follow the workshop will feature international experts on elliptic curves, modular forms, and related topics.

Funding from the National Science Foundation, the National Security Agency, and the Number Theory Foundation will make it possible for undergraduate and graduate students to attend the summer school and conference.

## June 2018

### Perspectives on the Riemann Hypothesis

Meeting Type: conference

Contact: see conference website

### Description

A meeting on the Riemann Hypothesis, and on the theory of the zeta-function and other L-functions.

### Mathematics is a long conversation: a celebration of Barry Mazur

Meeting Type: conference

Contact: see conference website

### Description

### NSF/CBMS Conference on “Applications of Polynomial Systems”

Meeting Type: conference

Contact: Greg Friedman

### Description

The conference will feature a series of ten lectures by Professor David Cox on topics including elimination theory, polynomial systems in the real world, geometric modeling, geometric constraint theory, and chemical reaction networks. Follow up lectures will be given by other leading experts including Carlos D’Andrea, Jonathan Hauenstein, Hal Schenck, Jessica Sidman, and Alicia Dickenstein. The conference will also feature a problem session, software demonstration, and poster session.

The CBMS and NSF have generously provided funding for the conference, including funds for travel and lodging of attendees (NSF grant DMS-1741730) . To apply for funding, please visit the conference website. Graduate students, recent PhDs, and members of underrepresented groups in mathematics are especially encouraged to apply.

Sponsored by the Conference Board of the Mathematical Sciences, each five-day conference in the Regional Conference series features a distinguished lecturer who delivers ten lectures on a topic of important current research in one sharply focused area of the mathematical sciences; the lecturer subsequently prepares an expository monograph based upon these lectures. The principal lecturer for this conference will be David A. Cox, the William J. Walker Professor of Mathematics at Amherst College. Professor Cox is a world-renowned master expositor and award-winning author of several popular and highly-cited books in the mathematical area of applied algebraic geometry. Professor Cox’s lectures will discuss historical developments in this field in light of modern perspectives, leading right up to current research and applications to such diverse fields as computer aided design, rigidity of mechanical linkages, and chemical reaction networks. Each pair of lectures by Professor Cox will develop a chosen topic and be followed by a further lecture by a specialist he has hand-picked to provide a deeper look at the forefront of current work on that topic.

### Ecole jeunes chercheurs en théorie des nombres 2018

### Number Theoretic Methods in Hyperbolic Geometry

Meeting Type: conference

Contact: see conference website

### Description

The canonical example of an arithmetic lattice is the modular group PSL(2, Z), whose deep connections with geometry and number theory (among many other areas) have been of profound interest for well over a century. Geometric invariants of the modular surface—the quotient of the complex upper half-plane by PSL(2, Z)—are typically paired with objects of equally deep interest in number theory. For example, its volume in its metric of constant curvature -1 is naturally related to a special value of the Riemann zeta function, and the lengths of its closed geodesics are intimately related to class numbers and regulators of real quadratic fields. More generally, rigidity phenomena (Weil, Mostow, etc.) imply that similar connections exist between number theory and the geometry of higher-dimensional hyperbolic manifolds.

The primary focus during the workshop will be to introduce the participants to problems at the interface of geometry and number theory that are currently attracting significant interest, and provide them with the tools necessary to make progress on some open questions. General areas to be discussed include the Laplace eigenvalue spectra and geodesic length spectra of hyperbolic 2- and 3-manifolds, growth of the systole of a hyperbolic manifold, and the ‘realization problem’ for trace fields of hyperbolic 3-manifolds. The number theoretic techniques that we will use to address these problems make use of quaternion algebras over number fields, Mahler measures of algebraic integers, and classical results from multiplicative number theory. The ultimate goal of this workshop is to start a dialogue between young mathematicians from different backgrounds that will lead to new and long-lasting collaborations between fields that have a great deal to say to one another. No background in either subject is expected.

### Quantum integrability and quantum Schubert calculus

Meeting Type: conference

Contact: Scientific Programmes

### Description

This meeting will discuss the recent developments in Schubert calculus and representation theory, bringing together scientists working in algebra, geometry and topology and mathematical physics with the aim of building interdisciplinary contacts. The meeting is free to attend; participants just have to cover their accommodation, travel and subsistence.

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

Meeting Type: conference

Contact: Ahmed Abbes

### Description

### Early Career Workshop: Coding theory, cryptography, and number theory

Meeting Type: conference, workshop

Contact: Gretchen Matthews

### Description

Each summer Clemson University will host a one-week Early Career Research Workshop (ECRW) in Coding Theory, Cryptography, and Number Theory, aimed at postdocs and junior faculty. Three prominent researchers that have demonstrated success in mentoring postdocs will be invited to lead research teams consisting of postdocs and junior faculty (and possibly advanced graduate students when appropriate.) This workshop will help postdocs and junior faculty foster new collaborations and expand their existing research programs, both essential ingredients to launching and maintaining a healthy research program.

We will fund 9 participants for the ECRW with up to $500 for travel, per diem at $25/day for 6 days, and accommodations at $100/night for 5 nights. The funding is restricted to citizens or permanent residents of the US.

### "From the Fundamental Lemma to Discrete Geometry, to Formal Verification" conference in honor of Thomas C. Hales

Meeting Type: conference

Contact: Chris Kapulkin

### Description

### Communicating Mathematics Effectively

Meeting Type: workshop

Contact: Bianca Viray, John Voight

### Description

This week-long workshop is for late-stage graduate students and early-stage postdocs in number theory to learn and develop strategies for giving clear, motivated, and informative talks. While some of the workshop will focus on basic skills like good boardwork and eye contact, the majority of the workshop will be focused on how to effectively convey mathematical ideas to people outside of one's particular specialty in number theory. There will be multiple small breakout sessions where faculty mentors (including the organizers) will give feedback on talks and discuss concrete strategies for preparing and giving talks.

### The 13th Brauer group conference

Meeting Type: conference

Contact: Daniel Krashen, Kelly McKinnie

### Description

This meeting will be loosely structured around the Brauer Group and related topics. In the tradition of past Pingree Park Brauer group meetings, we are happy to welcome families, graduate students and young researchers, and hope to provide ample time to informally discuss mathematics and explore the beautiful Rocky Mountains.

### Homotopy Theory Summer Berlin

Meeting Type: 2 workshops with introductory summer schools

Contact: A. Blumberg, T. Gerhardt, M. Hill, M. Levine, H. Reich, O. Röndigs, P.A. Østvær

### Description

The Homotopy Theory Summer Berlin 2018 will consist of two workshops with introductory summer schools on algebraic K-theory, equivariant and motivic homotopy theory. It is supported by the Berlin Mathematical School, the DFG Priority Program 1786 "Homotopy theory and algebraic geometry", and the RCN Frontier Research Group "Motivic Hopf equations". The list of confirmed participants includes:

- Stefan Schwede (Summer school lecturer)
- Florian Strunk (Summer school lecturer)
- Georg Tamme (Summer school lecturer)
- Marco Varisco (Summer school lecturer)
- Alexey Ananyevskiy
- Ben Antieau
- Aravind Asok
- Tom Bachmann
- Jean Fasel (tentative)
- Grigory Garkusha
- Bertrand Guillou
- Jeremiah Heller
- Marc Hoyois
- Dan Isaksen
- Akhil Mathew
- Haynes Miller (tentative)
- Fabien Morel (tentative)
- Thomas Nikolaus (tentative)
- Justin Noel
- Kyle Ormsby (tentative)
- Ivan Panin
- Birgit Richter (tentative)
- Christian Schlichtkrull
- Markus Spitzweck
- Vesna Stojanoska
- Kirsten Wickelgren
- Ben Williams
- Glen Wilson
- Inna Zakharevich

We look forward to seeing many of you in Berlin during this event!

The organizers:

Andrew Blumberg, Teena Gerhardt, Mike Hill, Marc Levine, Holger Reich, Oliver Röndigs, Paul Arne Østvær

### Algebraische Zahlentheorie

Meeting Type: invitational workshop

Contact: see conference website

### Description

Organisers

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

### Automorphic forms on reductive groups and their covers: A conference in honour of Solomon Friedberg

Meeting Type: conference

Contact: see conference website

### Description

### L-Functions: Open Problems and Current Methods

Meeting Type: summer school

Contact: see conference website

### Description

L-functions are among the key unifying themes of modern number theory: seemingly ubiquitous, one finds them naturally associated to number fields, automorphic forms, abelian varieties, Artin representations, and more.

Central analytic questions about L-functions include their moments, size, non-vanishing, distribution of zeros and have been key to expanding our understanding of the distribution of prime numbers, arithmetic statistics, equidistribution of special points and periods, Diophantine equations, random matrix theory, and quantum chaos. In turn, exciting progress on L-functions is being made using and often combining tools ranging from as far as exponential sums, oscillatory integrals, complex and p-adic analysis to spectral analysis, trace formulas, and algebraic geometry.

This summer school aims to introduce graduate students and young postdocs to a variety of approaches and techniques in the analytic theory of L-functions. The school will emphasize the thinking and intuition underlying various approaches, their use in practice and adaptability to a range of situations, and the organic unity of the subject.

Speakers:

```
Valentin Blomer (Universität Göttingen)
Philippe Michel (Ecole Polytechnique Fédérale de Lausanne)
Djordje Milićević (Bryn Mawr College)
Caroline Turnage-Butterbaugh (Duke University)
Matthew Young (Texas A&M University)
```

### Torsion groups and Galois representations of elliptic curves

Meeting Type: conference

Contact: Filip Najman

### Description

The purpose of this conference is to bring together experts working on torsion groups and Galois representations attached to elliptic curves and related areas.

### Arithmetic and geometry of local and global fields

Meeting Type: conference

Contact: see conference website

### Description

Hội nghị sẽ đề cập đến nhiều hướng nghiên cứu chính của lý thuyết số và hình học đại số đang được phát triển mạnh tại châu Á. Ba chủ đề chính sẽ xoay quanh đa tạp Shimura, đối đồng điều p-adic và lý thuyết số trên trường hàm.

## July 2018

### International Conference on Algebra and Related Topics (ICART 2018)

Meeting Type: conference

Contact: Driss Bennis

### Description

We are pleased to announce the "first edition" of the International Conference on Algebra and Related Topics (ICART 2018).

ICART 2018 will be held from the 2nd to the 5th of July 2018 at the Faculty of Sciences, Mohammed V University in Rabat, Morocco.

ICART 2018 will cover various research areas presented in the following three sessions:

- Applied and Computational Homology in Topology, Algebra and Geometry (ACHTAG)
- Homological Algebra, Modules, Rings and Categories (HAMRC)
- Linear and Multilinear Algebra and Function Spaces (LMAFS)

Please, see the website* http://www.fsr.ac.ma/icart2018/ to get more information including the list of Plenary Speakers.

Proceedings. http://fsr.um5.ac.ma/icart2018/proceedings.html

The proceedings of ICART2018 will be published in :

• A special issue of "Algebra Colloquium" for the sessions "Homological Algebra, Modules, Rings and Categories" and "Applied and Computational Homology in Topology, Algebra and Geometry".

• A volume in "Contemporary Mathematics" for the session "Linear and Multilinear Algebra and Function Spaces".

Please keep the following dates in mind as you prepare to attend icart2018 :

• Submission of Abstracts: April 20th, 2018.

• Early Registration Fee Payment: April 30th, 2018.

• Late Registration Fee Payment: Mai 31st, 2018.

### p-adic Langlands Correspondence, Shimura Varieties and Perfectoids

Meeting Type: conference

Contact: see conference website

### Description

Since its introduction in the 70’s, the Langlands program is now the center of major developments with striking arithmetic applications. Since recently and in particular with the works of P. Scholze, a p-adic version of this program has emerged which concentrates a large number of arithmeticians.

This conference organised inside our ANR project aims to gather mathematicians interested in the last developments of the Langlands program and in particular the young researchers. Through about 20 talks, we aim to present the more interesting recent results and cover a large field of subjects.

The costs of the stay will be covered by the CIRM and ANR: young colleagues who would need some funds for travelling should write to us.

### K-theory, Hecke Algebras and Representation theory

Meeting Type: conference

Contact: Haluk Sengun

### Description

This is a conference that will focus on new and developing links between operator K-theory and representation theory. More specifically, the meeting will consider the following themes:

- recent advances in operator K-theory and representation theory for affine Hecke algebras, with applications to the ABPS conjecture for p-adic groups, the Baum-Connes conjecture and the local Langlands correspondence,
- new constructions linking KK-theory, the Hecke algebras associated to arithmetic groups and automorphic forms,
- new approaches to tempered representation theory for real groups via operator algebras and noncommutative geometry,
- progress on the 'Mackey bijection' between the irreducible representations of real groups and the irreducible representations of associated Cartan motion groups.

We believe that the time is ripe to expect fruitful interaction among the above mentioned research areas. We tried to push the synergistic aspects of the meeting further by bringing together a balance of experts who work in representation theory, harmonic analysis, and automorphic forms with experts in noncommutative geometry and operator K-theory. Speakers will be encouraged to present open problems accessible across boundaries, and touch upon possible new points of contact between the different subjects represented at the meeting.

### Summer School on explicit and computational approaches to Galois representations

Meeting Type: summer school

Contact: Shaunak Deo, Ilker Inam, Antonella Perucca

### Description

The aim of the summer school is to provide foundational knowledge necessary for carrying out independent research on explicit and/or computational aspects of Galois representations. It is especially aimed at PhD candidates, but more advanced researchers as well as advanced Master students are welcome. Women are explicitly encouraged to participate in the Summer School!

### Workshop on Galois Representations

Meeting Type: workshop

Contact: see conference website

### Description

Main topics of the workshop will include recent modularity theorems, families of Galois representations, results on lifting and derived methods.

### Berkovich spaces 30 years

Meeting Type: conference

Contact: see conference website

### Description

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

Meeting Type: conference

Contact: Hugo Chapdelaine, Antonio Lei, Claude Levesque

### Description

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

### Homotopy Theory and Arithmetic Geometry: Motivic and Diophantine Aspects

Meeting Type: summer school

Contact: see conference website

### Description

The focus of this research school is on three major advances that have emerged lately in the interface between homotopy theory and arithemic: cohomological methods in intersection theory, with emphasis on motivic sheaves; homotopical obstruction theory for rational points and zero cycles; and arithmetic curve counts using motivic homotopy theory. The emergence of homotopical methods in arithmetic represents one of the most important and exciting trends in number theory, and the lectures will give a gentle introduction to this highly technical area.

The three main lecture course topics are:

Cohomological methods in intersection theory Lecturer: Denis-Charles Cisinski (Regensburg) Assistant: Chris Lazda (Amsterdam)

Homotopical manifestations of rational points and algebraic cycles Lecturer: Tomer Schlank (HUJ) Assistant: Ambrus Pal (Imperial)

Arithmetic enrichments of curve counts Lecturer: Kirsten Wickelgren (Georgia Tech) Assistant: Frank Neumann (Leicester)

The lecture courses will be supplemented by tutorial sessions and guest lectures by Paul Arne Østvær (Oslo), Jon Pridham (Edinburgh) and Vesna Stojanovska (Illinois at Urbana-Champaign)

### AGRA 2018, a two-week school on Arithmetic, Groups and Analysis

Meeting Type: Summer school

Contact: see conference website

### Description

This will be a two-week school, following the lead of the previous two ones: AGRA I in Santiago, Chile, 2012 and AGRA II in Cusco, Peru 2015. The main aim of the series is the development of number theory (in the broadest sense) as an area of research in South America.

### Algorithmic Number Theory Symposium ANTS-XIII

Meeting Type: conference

Contact: see conference website

### Description

### Witt Vectors, Deformations, and Absolute Geometry

Meeting Type: conference

Contact: see conference website

### Description

### Explicit Methods in Number Theory

Meeting Type: invitational workshop

Contact: see conference website

### Description

Organisers

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

### Young Researchers in Mathematics (YRM) 2018

Meeting Type: conference

Contact: see conference website

### Description

Young Researchers in Mathematics is an annual conference bringing together communities of PhD students, postdocs, and other young researchers from all areas of mathematics. There will be a mixture of invited speakers, workshops, and contributed talks from a number of different topics within mathematics and related industry, as well as opportunities to meet and socialise with peers. This summer, we look forward to meeting you at the University of Southampton, 23 July-26 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.

### USC K-theory Summer School 2018 - Computations in stable motivic homotopy theory

Meeting Type: Summer School

Contact: Aravind Asok

### Description

**When**: July 31 - August 3, 2018

**Where**: The University of Southern California

**What**: The theme of the summer school is ``Computations in stable motivic homotopy theory." For more precise information see the webpage of the summer school.

**Who**: The intended audience is graduate students and postdocs interested in the subject.
Limited funding is available to support travel to and housing at the summer school. Please register at the webpage for the summer school to request funding. Priority for funding requests will be given to those applications complete before July 1, 2018.

**Organizers**: Aravind Asok and Oliver Röndigs

## August 2018

### International Congress of Mathematicians

Meeting Type: international congress

Contact: see conference website

### Description

Satellite conferences will appear later with their own entries.

### New Trends in Analytic Number Theory

Meeting Type: summer school

Contact: see conference website

### Description

Analytic number theory is the branch of mathematics in which ideas and methods of real and complex analysis are brought to bear on problems about integer numbers. In particular, analytic techniques have led to major advances in number theory and helped to solve several important and difficult questions about integers. One of the crowning achievements of analytic number theory was the proof of the prime number theorem by using properties of the Riemann zeta function. In the last few years, analytic number theory has flourished and we have seen an upsurge of activity worldwide related to analytic number theory, prime number theory, and solutions to equations.

In this research school young researchers will learn key ideas and techniques of the field and about the most recent results and future directions of the field. It will benefit researchers having a background in number theory as well as those from parallel areas such as random matrix theory, Diophantine geometry and function field arithmetic. This research school will focus on three related topics and developments in analytic number theory:

- (i) classical analytic number theory, prime number theory and its recent developments
- (ii) Diophantine geometry and Hardy-Littlewood circle method
- (iii) analytic number theory in the function field context

These are active research areas where techniques from analysis (real, complex and Fourier analysis) plays an important role in trying to solve questions about integer numbers. Six experts in analytic number theory and its applications will conduct three mini-courses. To complement the mini-courses, distinguished speakers with substantial reputations in prime number theory, elliptic curves, additive combinatorics and random matrix theory will give an overview and research lectures on recent advances in the field.

### Tropical geometry and moduli spaces

Meeting Type: conference

Contact: see conference website

### Description

In just the past few years, there have been a number of significant advances in building explicit links between tropical geometry and the algebraic geometry of moduli spaces, especially for curves and abelian varieties, using skeletons of nonarchimedean analytic spaces as a bridge between the two. These links explain many older correspondence theorems, from the beginnings of tropical enumerative geometry, and are being used to establish new correspondences and to prove new enumerative results of classical flavor, e.g. for counting curves with fixed invariants, and to prove degeneration formulas for logarithmic Gromov–Witten invariants as part of a broader program linking tropical geometry to mirror symmetry. At the same time, new algebraic foundations are emerging for scheme-theoretic tropical geometry, built out of the idempotent semirings studied by Brazilian mathematician and theoretical computer scientist Imre Simon.

We plan to use the gathering of a vast number of mathematicians for the 2018 ICM in Rio de Janeiro as an opportunity to bring together international and local experts working on tropical geometry, moduli spaces, and nonarchimedean analytic geometry for a conference that will include research talks by leading experts along with mini-courses to help graduate students and early career mathematicians enter this young and very promising area of mathematics.

There will be limited funding for the workshop, with a preference for young participants and participants from Latin America and developing countries.

### Arithmetic Geometry, Number Theory, and Computation

Meeting Type: conference

Contact: Bjorn Poonen, Andrew Sutherland

### Description

### Arithmetic Algebraic Geometry: A conference in honor of the 60th Birthday of Grzegorz Banaszak

Meeting Type: conference

Contact: see conference website

### Description

### Arithmetic and geometry of cubic hypersurfaces

Meeting Type: conference

Contact: see conference website

### Description

### Nairobi Workshop in Algebraic Geometry

Meeting Type: conference

Contact: see conference website

### Description

## September 2018

### Varieties: Arithmetic and Transformations

Meeting Type: conference

Contact: see conference website

### Description

Focus points

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

### Stark's Conjectures, Iwasawa theory and related topics

Meeting Type: Workshop

Contact: Henri Johnston, Andreas Nickel

### Description

See website.

### Arithmetic of Differential Equations

Meeting Type: summer school

Contact: see conference website

### Description

Teachers:

```
Frits Beukers (Utrecht)
Duco van Straten (Mainz)
Kiran S. Kedlaya (UC San Diego)
```

### School and Conference "Motives in St. Petersburg"

Meeting Type: conference, summer school

Contact: Alexey Ananyevskiy, Grigory Garkusha, Ivan Panin

### Description

### Women in Automorphic Forms

Meeting Type: conference

Contact: see conference website

### Description

This is a conference in number theory and arithmetic geometry specially addressed to female mathematicians working in these areas. However, anybody interested in these topics is kindly invited to attend. Invited Speakers Include

```
Kathrin Bringmann (U Köln)
Miranda Cheng (U Amsterdam)
Jessica Fintzen (U Michigan/U Cambridge)
Özlem Imamoglu (ETH Zurich)
Judith Ludwig (U Bonn)
Jasmin Matz (Hebrew U)
Kathrin Maurischat (U Heidelberg)
Anke Pohl (U Jena)
Christelle Vincent (U Vermont)
```

### Arithmetic Ramsey Theory

Meeting Type: conference

Contact: see conference website

### Description

Whilst in Manchester, Paul Erdős co-authored two formative papers in Ramsey theory:

- 'A combinatorial theorem in geometry' (with G. Szekeres, 1935), giving a new proof of Ramsey's theorem.
- 'On some sequences of integers' (with P. Turán, 1936), laying the foundation for density results over arithmetic sets.

Some 80 years later, we would like to commemorate this and subsequent discoveries in additive combinatorics, continuing the celebration of the return of the number theory group to Manchester initiated by Diophantine Problems.

The central topic of the conference concerns the existence of structure within large arithmetic sets (broadly interpreted). In particular:

- Density bounds for sets lacking arithmetic configurations (Roth's theorem, Szemerédi's theorem, the cap-set problem and the polynomial method).
- Existence of arithmetic configurations in relatively dense sets (Szemerédi's theorem in the primes, combinatorial theorems in sparse (pseudo)random sets).
- Partition regularity of arithmetic configurations (monochromatic sums and products, regularity of non-linear equations).
- Applications of higher-order Fourier analysis to all of the above, including counting solutions to equations in arithmetic sets of interest.

Enquiries can be sent to the organisers at arithmeticramsey@gmail.com.

### Arithmetic Geometry : l-adic and p-adic aspects

Meeting Type: conference

Contact: Ahmed Abbes, Takeshi Saito

### Description

### International Summer School on Arithmetic Geometry

Meeting Type: summer school

Contact: Dino Festi, Ariyan Javanpeykar, Davide Cesare Veniani

### Description

This is a Summer School of the SFB/TRR 45 Bonn-Essen-Mainz financed by the DFG (Deutsche Forschungsgemeinschaft). It will take place from September 10th until September 14th, 2018 at the Università degli studi di Salerno (Italy).

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

The school consists of four mini-courses of four 1-hour classes each, plus three research talks. During the week, two sessions for questions of the students to the lecturers of the mini-courses are also scheduled.

Lecturers: Jarod Alper, Ekaterina Amerik, Michel Brion, Jason Starr.

Research speakers: Olivier Benoist, Simone Diverio, Erwan Rousseau.

### Joint meeting of the Italian Mathematical Union, the Italian Society of Industrial and Applied Mathematics and the Polish Mathematical Society

Meeting Type: conference

Contact: Karol Szczypkowski

### Description

UMI-SIMAI-PTM Mathematical Meeting is a joint initiative of the Polish Mathematical Society (Polskie Towarzystwo Matematyczne), the Italian Mathematical Union (Unione Matematica Italiana) and the Italian Society of Industrial and Applied Mathematics (Società Italiana de Matematica Applicata e Industriale).

The meeting aims at continuation of the tradition of bilateral meetings held in the last years by the Polish Mathematical Society together with other national societies. Mathematicians from other countries are also cordially invited to participate. The meeting will be hosted by the Faculty of Mathematics and Computer Science of the University of Wrocław and the Faculty of Mathematics of Wrocław University of Science and Technology. Its program will cover topics pertaining to mathematical research conducted in Italy and Poland with a special focus on the applications. It will start on Monday morning September 17, 2018 and end its Scientific Program in the afternoon on Thursday, September 20, 2018. Thursday night and two following days (Friday and Saturday) may be devoted to social activities up to a personal choice (excursions, sightseeing, town's cultural events, shopping), as well as for individually organized scientific activities.

### Open questions in number theory and cryptography

Meeting Type: conference

Contact: see conference website

### Description

In addition to bringing together mathematicians and cryptographers to discuss open questions, this conference will celebrate Alice Silverberg's 60th birthday.

### School in Arithmetic Geometry

Meeting Type: summer school

Contact: see conference website

### Description

### Varieties and Group Actions

Meeting Type: summer school, conference

Contact: see conference website

### Description

Confirmed lecturers:

```
Ana-Maria Castravet (Northeastern University), title: Mori Dream Spaces and Blow-ups,
Michel Brion (Institut Fourier, Grenoble), title: Automorphism groups in algebraic geometry,
Zach Teitler (Boise University), title: Waring rank.
```

Organizers: Jarosław Buczyński (Institute of Mathematics, Polish Academy of Sciences), Nathan Ilten (Simon Fraser University), Tomasz Mańdziuk (University of Warsaw), Jarosław Wiśniewski (University of Warsaw)

The titles of lecture series are provisional.

The workshop (Thursday-Saturday) will be devoted to more advanced research topics presented by invited speakers and participants. Afternoons will be devoted to discussions groups. Possible subjects: Mori Dream Spaces, torus actions, homogeneous spaces, contact Fano manifolds, Hilbert schemes, rational curves on manifolds, secant varieties, tensor and Waring ranks with their applications.

The event is supported by the Banach Center, the Targeted Grant to Institutes of Simons Foundation and by Polish Ministry of Science and Higher Education (MNiSW).

It is a part of the Simons Semester VAT (Varieties and Transformations).

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

Meeting Type: conference

Contact: see conference website

### Description

## October 2018

### Conference on Arithmetic Algebraic Geometry, On the occasion of Michael Rapoport’s 70th birthday

Meeting Type: conference

Contact: see conference website

### Description

### Cohomology of Algebraic Varieties

Meeting Type: conference

Contact: Anna Cadoret, François Charles, Cyril Demarche, Bruno Klingler, Ben Moonen

### Description

This conference will be the mid-project meeting of the A.N.R. project ECOVA "Cohomological study of algebraic varieties". The aim is to gather together algebraic and arithmetic geometers whose research focusses on cohomological aspects. We intend to cover the wide spectrum of the ECOVA project, including motivic, geometric and complex Hodge-theoretic, p-adic aspects, non-archimedean and arithmetic aspects.

## November 2018

### New Developments in the Theory of Modular Forms over Function Fields

Meeting Type: conference

Contact: Mihran Papikian

### Description

### Syntomic cohomology and p-adic Hodge theory

Meeting Type: school

Contact: see conference website

### Description

## December 2018

### On the Langlands Program: Endoscopy and Beyond

Meeting Type: thematic program

Contact: see conference website

### Description

This programme will focus on the study of the Langlands functoriality conjecture, including the endoscopy theory and the cases beyond endoscopy.

For the endoscopy case, Langlands functoriality is established by using the trace formula approach in general. Some special cases can also be established by the converse theorem-integral representation approach, and the automorphic integral transform approach.

Based on those successful cases, several new approaches are proposed. The key idea is to construct certain appropriate automorphic kernel functions and study them in various ways in order to establish functorial transfers for automorphic forms in the relative general setting.

These bring us the following four topics of the program:

```
Refined structures and properties for endoscopy theory: local and global.
Various types of trace formulas, generalized Fourier transforms and Poisson summation formulas, and applications.
Explicit constructions of certain Langlands functorial transfers via integral transformations.
Extension of the existing theory in the Langlands program to covering groups.
```

The goal of the program is to bring together experts researching in automorphic kernel functions to foster interaction, collaboration and the exchange of ideas on the new approaches. It aims to develop those approaches that will provide us further insights and progress, and lead to an eventual resolution of the Langlands functoriality conjectures.

## January 2019

### Arithmetic of Shimura Varieties

Meeting Type: conference

Contact: see conference website

### Description

### 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.

### Connections for Women: Derived Algebraic Geometry, Birational Geometry and Moduli Spaces

Meeting Type: conference

Contact: see conference website

### Description

This workshop will be on different aspects of Algebraic Geometry relating Derived Algebraic Geometry and Birational Geometry. In particular the workshop will focus on connections to other branches of mathematics and open problems. There will be some colloquium style lectures as well as shorter research talks. The workshop is open to all.

### Introductory Workshop: Derived Algebraic Geometry and Birational Geometry and Moduli Spaces

Meeting Type: conference

Contact: see conference website

### Description

The workshop will survey several areas of algebraic geometry, providing an introduction to the two main programs hosted by MSRI in Spring 2019. It will consist of 6 expository mini-courses and 8 separate lectures, each given by top experts in the field.

The focus of the workshop will be the recent progress in derived algebraic geometry, birational geometry and moduli spaces. The lectures will be aimed at a wide audience including advanced graduate students and postdocs with a background in algebraic geometry.

## February 2019

### Braids, Resolvent Degree and Hilbert’s 13th Problem

Meeting Type: conference

Contact: see conference website

### Description

Overview

HIL2019 web imageThe purpose of this workshop is to bring focused attention to Hilbert’s 13th problem, and to the broader notion of resolvent degree. While Abel’s 1824 theorem–that the general degree n polynomial is only solvable in radicals for n<4

is well known, less well known is Bring’s 1786 proof that a general quintic is solvable in algebraic functions of only one variable. Hilbert conjectured that for a general sextic, one needs algebraic functions of two variables, and that for a general degree 7 polynomial, one needs algebraic functions of three variables. More generally, it is natural to expect that as n → ∞ , so does the minimal number of variables needed to solve the general degree n polynomial. In a celebrated theorem, Arnol’d and Kolmogorov proved that, at the level of continuous functions, there is no local obstruction to reducing the number of variables to one. Thus, a resolution of Hilbert’s problem must lie deeper. Resolvent degree was introduced by Brauer in order to provide a rigorous statement of these conjectures. While no progress has yet been made on these conjectures, the study of resolvent degree is receiving renewed attention and an influx of ideas from related fields, including:

```
the theory of essential dimension
uniformization of moduli spaces
braid monodromy
p-adic Hodge theory
```

This workshop will bring together young and established researchers who work in these fields to explore topics related to Hilbert’s conjectures, to facilitate interaction between subdisciplines, and to lay the groundwork for future progress. The workshop will be organized around mini-courses by experts which will be aimed at 1) conveying the methods that can be brought to bear from each area, and 2) formulating problems concerning resolvent degree that seem particularly tractable using these methods.

### Non-Archimedean Geometry and Applications

Meeting Type: conference

Contact: see conference website

### Description

## March 2019

### Arizona Winter School: Topology and Arithmetic

Meeting Type: conference

Contact: see conference website

### Description

Speakers:

- Michael Hopkins
- Jacob Lurie
- Matthew Morrow
- Kirsten Wickelgren

### Derived algebraic geometry and its applications

Meeting Type: conference

Contact: see conference website

### Description

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

## April 2019

### Tropical Geometry: New Directions

Meeting Type: conference

Contact: see conference website

### Description

## May 2019

### Definability and decidability problems in number theory

Meeting Type: conference

Contact: see conference website

### Description

This workshop, sponsored by AIM and the NSF, will be devoted to definability and decidability problems in number theory.

The main topics for the workshop are

- H10 and existential definability of Z for Q and big subrings of Q.
- Decidability of the first-order and the existential theory in finite and infinite algebraic extensions of Q. The workshop will bring together mathematicians working in algebraic geometry, number theory, model theory and computability theory to work on problems in decidability/computability and definability in number theory.
- Definability of valuation rings over infinite algebraic extensions of Q and over function fields.

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.

### Recent Progress in Moduli Theory

Meeting Type: conference

Contact: see conference website

### Description

This workshop will be focused on presenting the latest developments in moduli theory, including (but not restricted to) recent advances in compactifications of moduli spaces of higher dimensional varieties, the birational geometry of moduli spaces, abstract methods including stacks, stability criteria, and applications in other disciplines.

## June 2019

### Arithmetic Geometry, Number Theory, and Computation II

Meeting Type: conference

Contact: Andrew V. Sutherland

### Description

### CMI-HIMR Summer School in Computational Number Theory

Meeting Type: summer school

Contact: Jennifer Balakrishnan, Tim Dokchitser

### Description

### Boston University-Keio University Workshop in Number Theory

Meeting Type: conference

Contact: Jennifer Balakrishnan, Masato Kurihara, Steve Rosenberg

### Description

## 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.

## August 2019

### Number Theory in the Americas

Meeting Type: collaboration conference

Contact: see conference website

### Description

In many Latin American countries, political instability, institutional weakness and a lack of government support for scientific research have hindered the development of mathematics. There have been signs of progress in recent years. In 2014, Brazilian mathematics received international recognition when Artur Avila became the first South American to be awarded a Fields Medal. In 2018, the International Congress of Mathematicians will be hosted in a Latin American country for the first time. Within the last five years, several major conferences, such as the Mathematical Congress of the Americas, the AGRA winter schools, and PRIMA 2017, have been organized with the specific aim of increasing mathematical activity in Latin American countries.

In spite of all of this progress, there is still room for improvement. Number theory research in South and Central America continues to be largely confined to geographically isolated pockets of activity, concentrated within a small number of subfields. Many of the strongest math students go abroad for their training, in some cases because they cannot find viable Ph.D. supervisors in the research areas that they hope to pursue in their home countries. In most areas, Latin American mathematicians continue to be poorly represented at major international conferences. The proposed workshop aims to address some of these issues. Our main objectives are as follows:

Facilitate collaboration between North, Central, and South American number theorists.

The primary aim of the proposed workshop is to promote collaboration between number theorists in North, Central, and South America. To do this, we will model our workshop after several other workshops that have been extremely successful at sparking new collaborations: the American Institute of Mathematics workshops, the AMS Mathematics Research Communities workshops, and the BIRS-sponsored Women In Numbers workshops. Participants will be divided into small project groups led by senior researchers. Most of the time during the workshop will be spent working on research in these project groups. The goal is for researchers to leave the workshop with the beginning of a research paper or, at least, with a list of good candidates for future collaborators and a deeper understanding of a timely subject.

Foster research in timely areas of number theory. All of our confirmed participants have impressive research track records, and several are leading mathematicians by world standards. All of our project groups are on areas central to current research in the field, and all of these areas can also be said to lie in the crossroads between number theory and other fields. In several cases, this requires little explanation: the study of the arithmetic of algebraic varieties lies in the intersection of number theory and algebraic geometry; the study of modular forms, which originated in complex analysis, has been essential to number theorists since Ramanujan. The Langlands program is inherently about building connections, particularly with representation theory.

Continuing with our list of topics: additive combinatorics is a relatively new name for an area that encompasses additive number theory, combinatorial arguments and probabilistic and ergodic ideas. The importance of analytical tools to number theory has been clear since Riemann, and the relevance of harmonic analysis and spectral theory has become clearer and clearer since the mid-20th century. Probabilistic arguments in number theory have been fruitful ever since Erd\H{o}s and Tur\'an. The relevance of ergodic theory and dynamical systems to number theory has been known at least since Furstenberg and Ratner. Geometry and number theory often give two different perspectives on arithmetic groups. In particular, spectral gaps and expanders are terrains where number theory, spectral theory and geometry meet.

Train young researchers. Rather than filling the workshop with invited participants, we will reserve some spaces for young researchers who can apply to work in project groups that match their interests. One of our aims is to provide specialized training for young researchers in Latin American countries and introduce them to interesting problems in areas that may not be well-represented in their home countries. In some cases, this will be their first experience with working on a collaborative project. We will take steps to create a supportive environment so that young researchers will feel encouraged by the experience. We will also hold several panel discussions on topics that will be of particular interest to young researchers (see the Overview for more details).

Provide mentoring opportunities for mathematicians who normally do not get to train young researchers. The project groups are designed to provide a vertical mentoring structure, enabling mathematicians at different stages of their careers to mentor one another. Some of our participants may be faculty members at institutions without Ph.D. programs, and some will come from countries where it is typical for the strongest students to go abroad for graduate school. Such participants will have an exceptional chance to mentor promising young researchers in their project groups.

Attract greater visibility for the work of Latin American number theorists. A growing number of Latin Americans are working in number theory. By assembling this group, we will demonstrate that there is, in fact, already a fair number of strong number theorists connected to Latin American countries. Holding our workshop at the CMO, and advertising it on the BIRS website, will lend them additional prominence.

Build a network of Spanish-speaking mathematicians. This workshop will provide the foundation for creating a global network of Spanish-speaking mathematicians. In particular, we plan to start an online community -- including a mailing-list and possibly a more visible database -- of self-identified Spanish-speaking number theorists from around the world, organized by research area, which we hope will be useful to future conference organizers. The defining criterion will be an ability and willingness to lecture and work in Spanish.

## September 2019

### New Developments in Representation Theory of p-adic Groups

Meeting Type: conference

Contact: see conference website

### Description

## October 2019

### Modularity and Moduli Spaces

Meeting Type: conference

Contact: see conference website

### Description

**Modularity**. Until relatively recently, the celebrated Taylor--Wiles method for establishing the automorphy of Galois representations carried several significant limitations. First, the method applied only to Galois representations expected to come from cohomological automorphic forms of regular weight. For classical modular forms this excludes the case of weight 1 forms. Second, the locally symmetric space in whose cohomology the automorphic form is expected to arise was required to be an algebraic variety (a Shimura variety). This excludes for instance the case of elliptic curves over imaginary quadratic fields, where the locally symmetric space is 3-dimensional, and so cannot even admit a complex structure. Finally, in the absence of results towards Serre's conjecture on the modularity of mod p Galois representations, the Taylor--Wiles method generally only establishes the potential automorphy of Galois representations, i.e., automorphy after a finite base change.

In a major breakthrough, Calegari--Geraghty have introduced a derived version of the Taylor--Wiles method which has the potential to remove the first two of these restrictions. To realize the potential of the Calegari--Geraghty method requires overcoming a number of significant challenges in the theory of automorphic forms and the arithmetic of Shimura varieties. For instance one needs to know the existence of Galois representations attached to torsion classes in the cohomology of locally symmetric spaces, as well as strong forms of local-global compatibility for those representations. Scholze [SchTorsion] (and independently Boxer [Boxer] in some special cases) has addressed the former, and work of Cariani--Scholze [CS] on the vanishing of torsion in the cohomology of non-compact Shimura varieties has made progress towards the latter. These advances already have remarkable applications, such as the proof of potential modularity of elliptic curves over imaginary quadratic fields, as well as the Sato--Tate conjecture for such curves [tenauthor].

In addition to examining these many important developments, the workshop will contemplate possible future improvements to the Calegari--Geraghty method, such as may come from incorporating the derived deformation theory of Galatius--Venkatesh [GV]. We will also explore the prospects for proving actual (rather than potential) modularity of elliptic curves over some CM fields. Another expected topic is work in progress by Boxer--Calegari--Gee--Pilloni on the potential automorphy of abelian surfaces, using the Calegari--Geraghty method, as well as Pilloni's ``higher Hida theory'' for coherent cohomology of Shimura varieties [Pilloni].

**Moduli of Galois representations**. In ongoing work, Emerton and Gee are constructing moduli stacks which parameterize p-adic Galois representations arising from p-adic local fields. In the classical deformation theory of Galois representations, one considers formal families of deformations of a fixed mod p Galois representation; in contrast, the Emerton--Gee stacks admit non-constant families of mod p Galois representations, raising the possibility of arguing by interpolating between them. Furthermore, thanks to the global geometry of these spaces one has more algebro-geometric tools at one's disposal to study them.

The Emerton--Gee moduli stacks are built out of moduli spaces of integral p-adic Hodge theory data. Several incarnations of p-adic Hodge theory play a role in constructing and understanding these spaces, including Breuil-Kisin modules, Wach modules, and Tong Liu's (ϕ,Gˆ)-modules. Understanding how these different theories interact should a play an important role in the further development of this field. There remains many open questions about these stacks. What are the components of the special fiber? Are they normal? Cohen--Macaulay? What kind of singularities do they have? What is the structure of the line bundles/coherent sheaves on these spaces? Answers to these questions would have broad implications for modularity and the p-adic Langlands program.

The geometry of the Emerton--Gee stacks is closely linked to the Breuil--M\'ezard conjecture, which first arose in the context of attempt to generalize the Taylor--Wiles method. This conjecture measures the complexity of local Galois deformation rings (i.e., the versal deformation rings at closed points of Emerton--Gee stacks) in terms of the modular representation theory of GLn;\ understanding the geometry of local deformation spaces is essential for proving modularity lifting theorems. The Breuil--M\'ezard conjecture is in turn closely connected to the so-called weight part of Serre's conjecture, which can be viewed as a step towards the conjectural p-adic local Langlands correspondence.

For example, Caraiani--Emerton--Gee--Savitt [CEGS] are able to use known results about the geometric Breuil--M\'ezard conjecture and the weight part of Serre's conjecture for GL2 to analyze the irreducible components of certain Emerton--Gee stacks and relate them to the modular representation theory of GL2. The moduli stack perspective has also already played a role in the proof of the weight part of Serre's conjecture in generic situations in higher dimensions [LLLM1, LLLM2] and in on-going work of Emerton--Gee on the existence of crystalline lifts of mod p representations.

Despite considerable progress (e.g.\ [Herzig, GHS]), there still is no unconditional statement of the weight part of Serre's conjecture beyond the case of GL2. The Emerton-Gee moduli stack may be helpful for understanding this conjecture, as illustrated by the work of [CEGS]. One objective of the workshop will be to formulate an unconditional weight part of Serre's conjecture in terms of the Emerton-Gee stack, and to understand how such a conjecture relates to modular representation theory and to the Breuil-M\'ezard conjecture.

Finally, there are already tantalizing hints, for instance the work of [EGS] proving Breuil's local-global compatibility conjecture for types in the p-adic Langlands program, that the Emerton--Gee moduli stacks will play an important role in future developments on the modularity of Galois representations. However, this avenue is as yet largely unexplored. Another goal of this workshop is to bring together leading experts involved in these two strands of research in order to explore the possible synergies between them.

**Local models for Galois deformation spaces**. Although the two flavors of moduli spaces (Shimura varieties, Galois deformation spaces) that we have contemplated in this proposal are rather different, Kisin [Kis09a] observed that there is a surprising and fundamental relation between them:\ namely, their singularities are both modeled by relatively simpler moduli spaces called local models of Shimura varieties. These local models have been studied extensively in the context arithmetic of Shimura varieties, so that much is known about their geometry. Kisin's observation led to improved modularity lifting theorems, which in turn played a key role in the eventual proof of Serre's original conjecture for GL2/Q.

Beyond dimension two, in order to study regular weight Galois deformation spaces, there is an additional condition which comes from a subtle analogue of Griffiths transverality in p-adic Hodge theory. In [LLLM1,LLLM2], Le--Le Hung--Levin--Morra give explicit presentations for certain potentially crystalline deformation rings with Hodge--Tate weights (0,1,2) by studying this Griffiths transversality condition, and as an application prove cases of the weight part of Serre's conjecture and other related conjectures in dimension three. In higher dimension, the connection with local models is weaker and does not capture the Griffiths transversality condition. Ongoing work of Le--Le Hung--Levin--Morra constructs local models for Galois deformation spaces in generic situations and will shed light on the structure of generic parts of the Emerton-Gee moduli stack. Further, there are mysterious connections between these local models and objects in geometric representation theory which have not yet been explored.

There are a number of parallels between the mod p and p-adic stories. A striking example of this is Breuil--Hellmann--Schraen's recent proof of a Breuil--M\'ezard type conjecture for locally analytic representations, which furthermore leads to a proof of the locally analytic socle conjecture of Breuil [BHS]. They study the geometry of a p-adic family of Galois representations called the trianguline variety. In another parallel to the mod p picture, they create a link between the geometry of these p-adic families to objects in geometric representation theory.

By sharing these new developments broadly with other experts in the field, the workshop aims to spur further development of connections between moduli of Galois representations and the geometry of (generalized) local models, and of parallels between the p-adic and mod p settings; and to contemplate what the implications might be for the geometry of Emerton--Gee stacks.

## November 2019

### Analytic Number Theory

Meeting Type: conference

Contact: see conference website

### Description

## June 2020

### Arithmetic Geometry, Number Theory, and Computation III

Meeting Type: conference

Contact: Andrew V. Sutherland

### Description

## August 2020

### Decidability, definability and computability in number theory

Meeting Type: research program

Contact: see conference website

### Description

This program is focused on the two-way interaction of logical ideas and techniques, such as definability from model theory and decidability from computability theory, with fundamental problems in number theory. These include analogues of Hilbert's tenth problem, isolating properties of fields of algebraic numbers which relate to undecidability, decision problems around linear recurrence and algebraic differential equations, the relation of transcendence results and conjectures to decidability and decision problems, and some problems in anabelian geometry and field arithmetic. We are interested in this specific interface across a range of problems and so intend to build a semester which is both more topically focused and more mathematically broad than a typical MSRI program.