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!

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

# Upcoming Meetings

## June 2022

### Rethinking Number Theory

ag.algebraic-geometry nt.number-theory
2022-06-20 through 2022-07-01
Virtual; USA

Meeting Type: workshop

Contact: see conference website

### Description

RNT-3 will be a remote collaborative research experience supported, in part, by the American Institute for Mathematics for the weeks of June 20 - July 1. The goal is for participants to learn new math, get to know colleagues, and have a joyful, affirming research experience. Workshop meetings will be planned around our busy schedules so that we can work on exciting research while also keeping up with our teaching and family responsibilities. Team leaders have planned projects for participants to work on during the workshop. You can read more about the projects here.

To ensure that all participants can share in this joyful research experience, we ask that all who apply to participate be committed to equity and justice. We will also make time to imagine a different way to do math: How could research seminars, postdoc positions, and graduate school be transformed to be comfortable to everyone? We will have a code of conduct for the workshop, which you can read here.

To participate in our workshop, please apply by the end of the day on May 15, 2022 The application is here.

RNT aims to foster diversity; we particularly encourage applications from historically underrepresented people in mathematics (including Black and Indigenous people, people of color, women, LGBTQ+ members of the community, and people with disabilities), scholars at undergraduate institutions, and in general scholars at all stages of their career who believe they would benefit from this experience. Please share this announcement with any groups, students, post docs, or scholars who might be interested in participating in this workshop. If you have questions, please email the organizers at: rethi[email protected]

### Homotopy theory with applications to arithmetic and geometry [European side]

ag.algebraic-geometry at.algebraic-topology gt.geometric-topology nt.number-theory
2022-06-27 through 2022-06-30
Max Planck Institute
Bonn; Germany

Meeting Type: twinned conference (see description)

Contact: Aaron Mazel-Gee

### Description

The field of homotopy theory originated in the study of topological spaces up to deformation, but has since been applied effectively in several other disciplines. Indeed, homotopical ideas lead to the resolution of several long-standing open conjectures, for instance on smooth structures on spheres, the moduli of curves, and the cohomology of fields. More recently, Bhatt, Morrow, and Scholze used homotopical methods to compare different cohomology theories for algebraic varieties, thereby resolving open questions in arithmetic geometry. In a similarly arithmetic vein, Galatius and Venkatesh initiated the study of Galois representations with homotopical means, whereas Clausen and Scholze revisited the foundations of analytic topology. These and other recent developments in the interface of arithmetic and topology opened up new lines of attack towards classical open questions, which sparked a wide range of current research activities. This conference intends to survey some of the most spectacular recent advances in the fields, thereby paving the way to new developments and future interactions. Our goal is to foster scientific exchange and collaboration between established researchers, emerging leaders, early career mathematicians, and graduate students.

This will be a split transatlantic conference taking place at the Fields Institute in Canada and the Max Planck Institute for Mathematics in Germany, with videoconferencing connections in place to help collaboration.

### Homotopy theory with applications to arithmetic and geometry [North American side]

nt.number-theory gt.geometric-topology at.algebraic-topology ag.algebraic-geometry
2022-06-27 through 2022-06-30
Fields Institute

Meeting Type: twinned conference (see description)

Contact: Aaron Mazel-Gee

### Description

The field of homotopy theory originated in the study of topological spaces up to deformation, but has since been applied effectively in several other disciplines. Indeed, homotopical ideas lead to the resolution of several long-standing open conjectures, for instance on smooth structures on spheres, the moduli of curves, and the cohomology of fields. More recently, Bhatt, Morrow, and Scholze used homotopical methods to compare different cohomology theories for algebraic varieties, thereby resolving open questions in arithmetic geometry. In a similarly arithmetic vein, Galatius and Venkatesh initiated the study of Galois representations with homotopical means, whereas Clausen and Scholze revisited the foundations of analytic topology. These and other recent developments in the interface of arithmetic and topology opened up new lines of attack towards classical open questions, which sparked a wide range of current research activities. This conference intends to survey some of the most spectacular recent advances in the fields, thereby paving the way to new developments and future interactions. Our goal is to foster scientific exchange and collaboration between established researchers, emerging leaders, early career mathematicians, and graduate students.

This will be a split transatlantic conference taking place at the Fields Institute in Canada and the Max Planck Institute for Mathematics in Germany, with videoconferencing connections in place to help collaboration.

### 7th IMA Conference on Numerical Linear Algebra and Optimization

ag.algebraic-geometry gm.general-mathematics
2022-06-29 through 2022-07-01
University of Birmingham
Birmingham; UK

Meeting Type: conference

Contact: Pam Bye

### Description

Early Bird Conference Fees IMA/SIAM Member - £395.00 Non IMA/SIAM Member - £450.00 IMA/SIAM Student - £215.00 Non IMA/SIAM Student - £225.00 Conference Fees will increase by £20 on 22 May 2022 Day Delegate rate: A Day Delegate rate is also available for this Conference if you would like to attend one of the scheduled Conference days. If you would like to find out more information about our Day Delegate rate, please contact us at [email protected]

Accommodation The IMA have booked accommodation at Edgbaston Park Hotel on hold for delegates on a first-come, first-serve basis. The room is £90 Single occupancy, B&B which will be available to book until 16/05/2022. If you are interested in booking at this rate, please contact the Conferences Department for the booking code.

Organising Committee Michal Kocvara, University of Birmingham (co-chair) Daniel Loghin, University of Birmingham (co-chair) Coralia Cartis, University of Oxford Nick Gould, Rutherford Appleton Laboratory Philip Knight, University of Strathclyde Jennifer Scott, Rutherford Appleton Laboratory Valeria Simoncini, University of Bologna Contact information For general conference queries please contact the Conferences Department, Institute of Mathematics and its Applications, Catherine Richards House, 16 Nelson Street, Southend-on-Sea, Essex, SS1 1EF, UK. E-mail: [email protected] Tel: +44 (0) 1702 354 020

## July 2022

### Azat Miftakhov Days – July 5-6, 2022

ag.algebraic-geometry mp.mathematical-physics rt.representation-theory
2022-07-05 through 2022-07-06
Paris - hybrid; France

Meeting Type: Special event

Contact: Ahmed Abbes

### Description

The second Azat Miftakhov Days will take place on Tuesday and Wednesday July 5-6, 2022, in solidarity with Azat Miftakhov, a mathematics graduate student from the Moscow State University who has been arbitrarily detained by Russian state authorities since February 2019.

• Tuesday July 5, 2022 from 4pm to 7pm Central European Summer Time (UTC+2) – online.

On the first day, we will honor the new generation of Russian mathematicians committed to human rights. The speakers are Ilya Dumanski (MIT), Alexander Petrov (Harvard) and Slava Rychkov (IHES). Their mathematical lectures will be broadcast live on Zoom and youtube.

• Wednesday July 6, 2022 from 5pm to 7pm Central European Summer Time (UTC+2) – hybrid.

On the second day, we will co-organize with Memorial Human Rights Center a panel to assess the human rights situation in Russia through the cases of persecuted academics. The panel will be hybrid, online and in person at the École normale supérieure in Paris, open to academics, human rights organizations and journalists.

Registration is mandatory both for participation online or in person. The registration form is available here (https://tinyurl.com/4wcwbrb6).

### Spec$(\overline{Q})$

ac.commutative-algebra ag.algebraic-geometry nt.number-theory
2022-07-06 through 2022-07-08
Fields Institute

Meeting Type: conference

Contact: see conference website

### Description

Spec(Q¯¯¯¯) is the first conference to celebrate and promote research advances of LGBT2Q mathematicians specialising in algebraic geometry, arithmetic geometry, commutative algebra, and number theory. This conference capitalises on recent thematic program successes in algebraic geometry at Fields, the Thematic Program on Combinatorial Algebraic Geometry (July 1 - December 31, 2016) and the Thematic Program on Homological Algebra of Mirror Symmetry (July 1 - December 31, 2019). Spec(Q¯¯¯¯) will create an empowering and engaging environment which provides LGBT2Q visibility in algebraic geometry, will support junior LGBT2Q academics, and will crystallise new collaborative networks for participants. Algebraic geometry, classically, is the study of the geometry of solutions of polynomial equations; through modern advances it has become an intersectional mathematical field, drawing from various aspects of algebra, number theory, geometry, combinatorics and even mathematical physics. This conference aims to highlight strong mathematical research in a wide array of algebraic geometry, broadly defined. The conference will feature some plenary talks by world-leading researchers from a range of areas of algebraic geometry. To facilitate new connections across the various threads of algebraic geometry, plenary talks at Spec(Q¯¯¯¯) will be aimed a general algebro-geometric audience.

This activity will bring together mathematicians spanning all academic ranks to create ideal networking and mentorship for LGBT2Q academics while disseminating key achievements of trans and queer algebraic geometers. Queer and trans academics often have a diffcult experience developing key collaborations and networks of trusted colleagues. Each research connection, grant, and application involves a conscious decision of how much of one’s queer/trans identity to disclose. This conference provides a safe space to develop ones network while removing these barriers. In such spaces, one can discuss mathematics with new colleagues while unbridled with many societal challenges that they face in mathematical communities. When a mathematician feels free to be themselves in all ways, they are able to immerse themselves in creative mathematical thought.

### Summer School on the Langlands Program

ag.algebraic-geometry nt.number-theory rt.representation-theory
2022-07-11 through 2022-07-29
IHES
Bures-sur-Yvette; France

Contact: see conference website

### Description

new description:

It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.

Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.

The summer school will attempt to bring these exciting new directions together and explore their interactions.

### Mid-South Algebraic Topology and Geometry Workshop

ag.algebraic-geometry at.algebraic-topology
2022-07-18 through 2022-07-20
Center for Mathematical Sciences, Huazhong University of Science and Technology
Online; China

Meeting Type: conference

Contact: Zhen Huan, Hao Sun

### Description

The workshop is online from July 18 to July 20th, 2022.

The algebraic topology and algebraic geometry in China are still developing, especially in the mid-south area. We hope we can help developing the math areas as much as we can. We plan to organize a 1-2 days workshop every quarter and a 3-5 days worshop every year in these areas. We also have online joint undergraduate seminars in algebraic topology and algebraic geometry.

If you are interested in giving a talk in one of the MSATG workshops, or you would like to give us some comments, feel free to contact us.

Huan, Zhen (Huazhong University of Science and Technology), [email protected]

Sun, Hao (South China University of Technology), [email protected]

## August 2022

### Galois representations and automorphic forms

ag.algebraic-geometry nt.number-theory rt.representation-theory
2022-08-07 through 2022-08-13
Banach Center
Będlewo; Poland

Meeting Type: conference

Contact: see conference website

### Description

none

ag.algebraic-geometry nt.number-theory
2022-08-08 through 2022-08-12

Contact: see conference website

### Description

The aim of the school is to give an overview of established results and current research on elliptic curves by covering the whole spectrum of techniques developed so far.

There will be 6 courses of 3 hours each plus exercises sessions.

• Course 1 : Analytic Methods - Alina Cojocaru
• Course 2 : Arithmetic Statistics - Jennifer Park
• Course 3 : Modularity-based Methods - Chao Li
• Course 4 : Points and Heights - Joseph Silverman
• Course 5 : Selmer Groups - Christian Wuthrich
• Course 6 : Torsion Points - Jan Vonk

### Fifteeth Algorithmic Number Theory Symposium, ANTS-XV

ag.algebraic-geometry nt.number-theory
2022-08-08 through 2022-08-12
University of Bristol
Bristol; USA

Meeting Type: conference

Contact: see conference website

### Description

The ANTS meetings, held biannually since 1994, are the premier international forum for the presentation of new research in computational number theory and its applications. They are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, algebraic geometry, finite fields, and cryptography.

### 3rd Workshop on Categorical Invariants and Higher Theory

ag.algebraic-geometry ct.category-theory mp.mathematical-physics rt.representation-theory sg.symplectic-geometry
2022-08-15 through 2022-08-19
outskirts of Berlin; Germany

Meeting Type: Workshop

Contact: Jasper van de Kreeke

### Description

Aim: To discuss categorical invariants and how to handle them with abstract methods. For 5 days, we are going to exchange ideas and hunt for new lines of thought.
Target group: Postdocs and PhD students.
Keynotes: Keynotes on the topic will be delivered by Dimitri Zvonkine, Junwu Tu and Fabian Haiden.
Setting: The event takes place in Jasper's backyard in the outskirts of Berlin. Facilities and meals are provided. The calm surroundings and liberal atmosphere enable a total focus on mathematical discussion.
US residents: US residents are more than welcome. The workshop includes an excursion in Berlin.

### Mordell 2022: 100 years of elliptic curves

ag.algebraic-geometry nt.number-theory
2022-08-15 through 2022-08-19
Cambridge University
Cambridge; UK

Meeting Type: conference

Contact: see conference website

### Description

The year 2022 marks the centenary of Mordell's 1922 paper "On the Rational Solutions of the Indeterminate Equations of the Third and Fourth Degrees", in which Mordell both established the foundational result in the arithmetic of elliptic curves (finite generation of rational points), and proposed what later became Mordell's Conjecture (and subsequently Faltings' Theorem).

In recognition of this anniversary, this conference will be a celebration of all aspects of the arithmetic of elliptic curves.

### Modular Forms in Number Theory and Beyond: Summer School

ag.algebraic-geometry nt.number-theory
2022-08-17 through 2022-08-19
Bielefeld University
Bielefeld; Germany

Contact: see conference website

### Description

The summer school aims to explore exciting applications of modular forms in different areas of Mathematics and provide a friendly and helpful environment to discuss and explore these concepts.

The summer school will consist of three courses given by Eugenia Rosu, Sven Möller, and a third researcher who will be confirmed later. Each course will consist of three lectures of 60-90minutes. There will be breaks in between to meet the other participants and discuss the content of the courses. More details will be shared closer to the date of the summer school.

The participants are expected to know the basics definition of (elliptic) modular forms.

### Modular forms in number theory and beyond

ag.algebraic-geometry nt.number-theory
2022-08-22 through 2022-08-26
Bielefeld University
Bielefeld; Germany

Meeting Type: conference

Contact: see conference website

### Description

Workshop for researchers from different backgrounds who are interested in modular forms in number theory and other mathematical disciplines organized by Claudia Alfes-Neumann, Michael Mertens and Markus Schwagenscheidt.

### XII International Conference of the Georgian Mathematical Union

ag.algebraic-geometry ap.analysis-of-pdes ca.classical-analysis-and-odes cv.complex-variables dg.differential-geometry fa.functional-analysis gm.general-mathematics gn.general-topology ho.history-and-overview lo.logic mp.mathematical-physics na.numerical-analysis pr.probability ra.rings-and-algebras st.statistics-theory
2022-08-29 through 2022-09-03
Shota Rustaveli State University (Batumi)
Batumi; Georgia

Meeting Type: conference

Contact: Tinatin Davitashvili

none

### Automorphic forms

ag.algebraic-geometry nt.number-theory rt.representation-theory
2022-08-29 through 2022-12-31
Rényi Institute
Budapest; Hungary

Meeting Type: thematic program

Contact: see conference website

### Description

The theory of automorphic forms is a dynamically expanding part of number theory with an increasing number of connections and applications to other branches of mathematics as well as physics. Research is driven by long standing conjectures and unexpected breakthroughs.

The purpose of this special semester is to bring together established researchers as well as those just starting their careers or studies. We would like to provide a rich and stimulating environment for interactions. There will be ample opportunity for the participants to present classical results and new developments. It is hoped that visits within this program will lead to further collaborations and progress.

### Curves over finite fields and arithmetic of K3 surfaces - A conference on the occasion of Jaap Top's 62nd Birthday

ag.algebraic-geometry nt.number-theory
2022-08-30 through 2022-09-01
University of Groningen
Groningen; Netherlands

Meeting Type: conference

Contact: see conference website

none

## September 2022

### Autumorphic forms

ag.algebraic-geometry nt.number-theory rt.representation-theory
2022-09-05 through 2022-09-09
Rényi Institute
Budapest; Hungary

Meeting Type: conference

Contact: see conference website

none

### School on Arithmetic Geometry on the occasion of Massimo Bertolini's 60th birthday

ag.algebraic-geometry nt.number-theory
2022-09-05 through 2022-09-09
Universitaet Duisburg-Essen
Essen; Germany

Meeting Type: school

Contact: see conference website

none

### Elliptic curves and modular forms in arithmetic geometry: a conference celebrating Massimo Bertolini's 60th birthday

ag.algebraic-geometry gm.general-mathematics nt.number-theory rt.representation-theory
2022-09-12 through 2022-09-16
University of Milan
Milan; Italy

Meeting Type: conference

Contact: Matteo Longo, Marco Adamo Seveso, Stefano Vigni, Rodolfo Venerucci.

none

### Summer School on Motivic Integration

ag.algebraic-geometry lo.logic
2022-09-12 through 2022-09-16
HHU Düsseldorf
Düsseldorf; Germany

Meeting Type: summer school

Contact: see conference website

### Description

The goal of this summer school is to introduce the participants to motivic integration and some of its applications. It is mainly aimed at PhD students and Postdocs who do work in an area around algebra and/or geometry, but who have not yet had any prior contact to this motivic integration. There will be three minicoures, which will explain the necessary tools and background material, give down-to-earth motivation and examples, and which will end with some interesting applications. In addition, there will be around ten one-hour talks about current research related to motivic integration. The summer school is part of the program of the DGF-funded research training group.

### Induction Course for New Lecturers in the Mathematical Sciences 2022

gm.general-mathematics at.algebraic-topology ag.algebraic-geometry gt.geometric-topology
2022-09-14 through 2022-09-15
Institute of Mathematics and its Applications
Cambridge; UK

Meeting Type: Induction course

Contact: Pamela Bye

### Description

Isaac Newton Institute for Mathematical Sciences, Cambridge 14 – 15 September 2022 https://ima.org.uk/19278/induction-course-for-new-lecturers-in-the-mathematical-sciences-2022/

# IMANewLecturers2022

Through a community initiative supported by the Institute of Mathematics and its Applications, the Isaac Newton Institute for Mathematical Sciences and the Heads of Departments of Mathematics Sciences (HoDoMS) and endorsed by the Royal Statistical Society and the London Mathematical Society, we are delighted to announce that in September 2022 the two‐day Induction Course for lecturers new to teaching mathematics and statistics within Higher Education will once again take place. Whilst arrangements may still be subject to change due to the ongoing Covid‐19 situation and any future Government guidance, we are currently preparing for the Induction Course to be delivered as an in‐person only activity to maximise the opportunities for informal networking and discussion that have long formed a highly‐valued part of this meeting.

The Induction Course for New Lecturers in the Mathematical Sciences has been designed by the mathematics community so that it is ideally suited for anyone who is new to or has limited experience teaching mathematics or statistics within UK higher education. It will be delivered by individuals with significant experience of teaching in the mathematical sciences and will focus upon the specific details and issues that arise in mathematics and statistics teaching and learning within higher education including topics such as:

• Lecturing. • Supporting student learning. • Making teaching interactive. • Assessment, examinations and feedback. • Linking teaching & research. • Using technology to enhance teaching and learning. • Using examples and mathematical problem solving. • Teaching statistics and its applications.

Additionally, there will be significant opportunities for delegates to discuss their own ideas, challenges and experiences with the session facilitators so that individual queries can be answered.

In the past, attendance has been recognised as contributing towards some introductory institutional programmes in learning and teaching for new staff, and for the 2022 Induction Course accreditation will be provided through the Institute of Mathematics and its Applications relative to the UK Professional Standards Framework for Teaching and Supporting Learning in Higher Education.

Timing The Induction Course takes place at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge and commences mid‐morning on the 14 September, and ends late‐afternoon on the 15 September. Accommodation will be offered at the University of Cambridge on the evening of the 14 September for any delegates who attend in person, although any in‐person attendance will be dependent upon the Covid‐19 situation at the time. As such, we reserve the right to make necessary changes to arrangements in response to Government legislation and guidance.

Session Facilitators Those leading the sessions at the Induction Course are all experienced teachers of mathematics within UK higher education. They include:

• Lara Alcock (Loughborough University) • Michael Grove (University of Birmingham) • Rachel Hilliam (Open University) • Kevin Houston (University of Leeds) • Joseph Kyle (University of Birmingham) • Steve Otto (The R&A) • Chris Sangwin (The University of Edinburgh) • Louise Walker (The University of Manchester) • John Mason (Open University) • Ulrike Tillmann (Isaac Newton Institute for Mathematical Sciences)

Induction Course Costs Following generous financial support from the Isaac Newton Institute for Mathematical Sciences, the Institute of Mathematics and its Applications and the Heads of Departments of Mathematical Sciences, we are able to offer the Induction Course at the following subsidised rates:

Full residential delegate rate* (Both days including all lunches, refreshments, Course dinner and accommodation on 18 September) £299

Two‐day delegate rate (Both days including all lunches, refreshments, Course dinner but no accommodation) £240 Day delegate rate (including lunch and refreshments) £95 Induction Course dinner (as a separate purchase) £56 * Please note that accommodation is allocated on a first‐come‐first served basis.

Registration Registration is now open via https://my.ima.org.uk/.

If you are an IMA Member or you have previously registered for an IMA conference, then you are already on our database. Please “request a new password” using the email address previously used, to log in. If you are attending the conference please use the hashtag #IMANewLecturers2022 and tag the IMA on socials!

ag.algebraic-geometry nt.number-theory
2022-09-19 through 2022-09-23

Meeting Type: conference

Contact: see conference website

none

### Women in Arithmetic Geometry

ag.algebraic-geometry nt.number-theory
2022-09-26 through 2022-09-30
University Heidelberg
Heidelberg; Germany

Meeting Type: conference

Contact: see conference website

### Description

It is a biannual conference intended to highlight recent developments in the work of women in arithmetic geometry, and to connect promising young mathematicians with outstanding senior colleagues. Participation is open to everybody. The event is part of the newly established collaborative research center „Geometry and Arithmetic of Uniformized Structures“ between the universities of Frankfurt, Heidelberg, Darmstadt, Mainz and Münster.

## October 2022

### Conference on Arithmetic Algebraic Geometry

ag.algebraic-geometry nt.number-theory
2022-10-03 through 2022-10-07

Meeting Type: conference

Contact: Ulrich Görtz

none

### Preliminary Arizona Winter School: Heights and Model Theory

ag.algebraic-geometry lo.logic nt.number-theory
2022-10-03 through 2022-11-11
University of Arizona
online; Antarctica

Contact: see conference website

### Description

The Preliminary Arizona Winter School (PAWS) is a virtual program on topics related to the upcoming AWS, with an intended audience of advanced undergraduate students and junior graduate students.

PAWS 2022 will consist of two concurrent six-week lecture series.

• Ronnie Nagloo: Introduction to model theory with applications

Model theory is a branch of mathematical logic dealing with abstract structures, historically with connections to other areas of mathematics. The developments, over the past several decades, have allowed for a strengthening of those connections as well as new striking applications to areas such as diophantine and analytic geometry, algebraic differential equations, and combinatorics. This course will serve as an introduction to the basics of model theory, with a view towards some of the above applications.

• Padmavathi Srinivasan: Heights in Diophantine geometry

The height of a rational number is a measure of its arithmetic complexity. For example, although the numbers 5 and 500000/100001 are close, the second is arithmetically more complex, and has a much larger height. The height of a rational number is easy to define -- it is simply the maximum of the absolute value of the numerator and the denominator when the number is expressed in lowest form. It is not immediately clear how one can extend this definition to more general algebraic numbers such as the squareroot of 2. In this series of lectures, we will develop the theory of heights of algebraic numbers, and present "Weil's height machine" for defining heights more generally for solutions to systems of polynomial equations in algebraic numbers (i.e., heights of algebraic points on varieties).

Height functions are a key tool in proving many important finiteness theorems in Diophantine Geometry. The main property of height functions is that there are only finitely many points of bounded height and degree on any given variety. Understanding how quickly the number of points grow as the height grows for various classes of varieties is an active area of research in number theory today! As an application of the theory of heights, we will prove the Mordell--Weil theorem for elliptic curves, namely that the set of rational solutions to cubic equations such as y^2 = x^3 - 2x + 2 is finitely generated.

Registration: You can apply for the program here. The deadline to apply is July 15th, 2022.

Each lecturer will be accompanied by graduate student assistants, who will be in charge of writing weekly problem sets and facilitating weekly, hour-long problem solving and discussion meetings with groups of students. Recommended background for the program is a first course in abstract algebra.

The school will feature an online (Zulip) discussion board where students can ask questions and interact with the speakers and assistants outside of scheduled meeting times.

We will facilitate additional virtual events, some purely social to build a community, and some more structured sessions on timely and pertinent topics like "What is graduate school in Math like?", "Tips for applying to graduate school this Fall," "How do I navigate the first year of graduate school?" "How do I look for an thesis advisor?", "How to get the most out of the upcoming AWS."

We encourage undergraduate students to take their PAWS course as an independent study with a faculty member at their home institution.

• Organizers: Renee Bell, Isabel Vogt, Hang Xue, with Alina Bucur, Brandon Levin, Anthony Várilly-Alvarado, and David Zureick-Brown.
• Funded by the National Science Foundation.

### Motives, quadratic forms and arithmetic

ag.algebraic-geometry kt.k-theory-and-homology nt.number-theory
2022-10-24 through 2022-10-28
Université d'Artois
Lens; France

Meeting Type: conference

Contact: Baptiste Calmès

### Description

A conference in honor of Bruno Kahn's 64th birthday

## November 2022

### Rationality, Moduli Spaces, and Related Topics

ag.algebraic-geometry
2022-11-07 through 2022-11-11
Nagoya University
Nagoya; Japan

Meeting Type: conference

Contact: Sho Tanimoto

none

## January 2023

### Arithmetic Statistics: Discovering and Proving Randomness in Number Theory

ag.algebraic-geometry nt.number-theory
2023-01-01 through 2023-06-30
Luminy; France

Meeting Type: thematic program

Contact: see conference website

none

### Algebraic Cycles, L-Values, and Euler Systems

nt.number-theory ag.algebraic-geometry
2023-01-17 through 2023-05-26
MSRI
Berkeley, CA; USA

Meeting Type: conference

Contact: see conference website

### Description

The fundamental conjecture of Birch and Swinnerton-Dyer relating the Mordell–Weil ranks of elliptic curves to their L-functions is one of the most important and motivating problems in number theory. It resides at the heart of a collection of important conjectures (due especially to Deligne, Beilinson, Bloch and Kato) that connect values of L-functions and their leading terms to cycles and Galois cohomology groups.

The study of special algebraic cycles on Shimura varieties has led to progress in our understanding of these conjectures. The arithmetic intersection numbers and the p-adic regulators of special cycles are directly related to the values and derivatives of L-functions, as shown in the pioneering theorem of Gross-Zagier and its p-adic avatars for Heegner points on modular curves. The cohomology classes of special cycles (and related constructions such as Eisenstein classes) form the foundation of the theory of Euler systems, providing one of the most powerful methods known to prove vanishing or finiteness results for Selmer groups of Galois representations.

The goal of this semester is to bring together researchers working on different aspects of this young but fast-developing subject, and to make progress on understanding the mysterious relations between L-functions, Euler systems, and algebraic cycles.

### Diophantine Geometry

ag.algebraic-geometry nt.number-theory
2023-01-17 through 2023-05-26
MSRI
Berkeley, CA; USA

Meeting Type: thematic program

Contact: see conference website

### Description

Number Theory concerns the study of properties of the integers, rational numbers, and other structures that share similar features. It is a central branch of mathematics with a well-known feature: it is often the case that easy-to-state problems in number theory turn out to be exceedingly difficult (e.g. Fermat’s Last Theorem), and their study leads to groundbreaking discoveries in other fields of mathematics.

A fundamental theme in number theory concerns the study of integer and rational solutions to Diophantine equations. This topic originated at least 3,700 years ago (as documented in babylonian clay tablets) and it has evolved into the highly sophisticated field of Diophantine Geometry. There are deep and fruitful interactions between Diophantine Geometry and seemingly distant fields such as representation theory, algebraic geometry, topology, complex analysis, and mathematical logic, to mention a few. In recent years, these connections have led to a large number of new results and, specially, to the partial or complete resolution of important conjectures in the field.

While the study of rational solutions of diophantine equations initiated thousands of years ago, our knowledge on this subject has dramatically improved in recent years. Especially, we have witnessed spectacular progress in aspects such as height formulas and height bounds for algebraic points, automorphic methods, unlikely intersection problems, and non-abelian and p-adic approaches to algebraic degeneracy of rational points. All these groundbreaking advances in the study of rational and algebraic points in varieties will be the central theme of the semester program “Diophantine Geometry” at MSRI. The main purpose of this program is to bring together experts as well as enthusiastic young researchers to learn from each other, to initiate and continue collaborations, to update on recent breakthroughs, and to further advance the field by making progress on fundamental open problems and by developing further connections with other branches of mathematics. We trust that younger mathematicians will greatly contribute to the success of the program with their new ideas. It is our hope that this program will provide a unique opportunity for women and underrepresented groups to make outstanding contributions to the field, and we strongly encourage their participation.

### Connections Workshop: Algebraic Cycles, L-Values, and Euler Systems

ag.algebraic-geometry nt.number-theory
2023-01-19 through 2023-01-20
MSRI
Berkeley, CA; USA

Meeting Type: conference

Contact: see conference website

### Description

The Connections Workshop features presentations by both leading researchers and promising newcomers whose research has contact with the interrelated topics of algebraic cycles, L-values, and Euler systems. The goal is to present a variety of diverse results, so as to forge new connections, foster collaborative projects, and establish mentoring relationships. While emphasis will be placed on the work of women mathematicians, the workshop is open to all researchers.

### Introductory Workshop: Algebraic Cycles, L-Values, and Euler Systems

ag.algebraic-geometry nt.number-theory
2023-01-23 through 2023-01-27
MSRI
Berkeley, CA; USA

Meeting Type: conference

Contact: see conference website

### Description

The Introductory Workshop aims to provide a coherent overview of current research in algebraic cycles, L-values, Euler systems, and the many connections between them. This includes the study of special cycles on Shimura varieties and moduli spaces of shtukas, integral representations of L-values and the construction of p-adic L-functions, and the construction of Euler systems from special elements in Chow groups or higher Chow groups of Shimura varieties. Workshop lectures will be organized into short lecture series, so as to allow each series to begin with expository lectures on foundational results before moving on to current research.

## February 2023

### Connections Workshop: Diophantine Geometry

ag.algebraic-geometry nt.number-theory
2023-02-02 through 2023-02-03
MSRI
Berkeley, CA; USA

Meeting Type: conference

Contact: see conference website

### Description

This workshop will highlight talks on various aspects of Diophantine Geometry. The goal of the workshop is to bring together researchers at different career stages and of various backgrounds in order to establish new collaborations and mentoring relationships. Although we will showcase the research of mathematicians who identify as women or gender minorities, this workshop is open to all.

### Introductory Workshop: Diophantine Geometry

ag.algebraic-geometry nt.number-theory
2023-02-06 through 2023-02-10
MSRI
Berkeley, CA; USA

Meeting Type: conference

Contact: see conference website

### Description

This workshop will feature expository lectures about current developments in Diophantine geometry. This includes the uniform Mordell—Lang for rational points on curves, the Andre—Oort conjecture for special points on Shimura varieties, and effective results via Chabauty method, and related topics in Arakelov theory, unlikely intersections, arithmetic statistics, arithmetic dynamics, and p-adic Hodge theory.

### Number Theory meets p-adic representations - a conference on the occasion of Peter Schneider's 70th birthday

ag.algebraic-geometry nt.number-theory rt.representation-theory
2023-02-13 through 2023-02-17
University Muenster
Muenster; Germany

Meeting Type: conference

Contact: Christopher Deninger, Eugen Hellmann

none

### Computational Number Theory

ag.algebraic-geometry nt.number-theory
2023-02-27 through 2023-03-03
Centre International de Rencontres Mathématiques
Luminy; France

Meeting Type: conference

Contact: see conference website

### Description

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

On the one hand, various topics where explicit computations have been the key for proving important results will be presented. These will be found in the context of modular forms, the study of rational points, as well as results towards the Birch and Swinnerton-Dyer conjecture. On the other hand, we will also focus on recently stated conjectures, for example the paramodular conjecture by Brumer and Kramer, and challenge participants to exhibit new examples to support such conjectures (in the case of the paramodular conjecture only one non trivial example is currently known).

We expect that the colloquium will lead to the emergence of new ideas and methods at the interface of these different fields, to new results as well as to new projects and collaborations.

This conference will be organized with the support of the National Research Agency in the framework of the project "MELODIA".

## March 2023

### Arizona Winter School: Unlikely Intersections

nt.number-theory ag.algebraic-geometry
2023-03-04 through 2023-03-08
University of Arizona
Tucson, AZ; USA

Contact: see conference website

### Description

Speakers:

• Laura DeMarco (Chicago)
• Jonathan Pila (Oxford)
• Thomas Scanlon (Berkeley)
• Jacob Tsirmerman (Toronto)

### Shimura Varieties and L-functions

ag.algebraic-geometry nt.number-theory rt.representation-theory
2023-03-13 through 2023-03-17
MSRI
Berkeley, CA; USA

Meeting Type: conference

Contact: see conference website

### Description

The topical workshop will be dedicated to Shouwu Zhang, to mark the occasion of his 60th birthday, and to honour his numerous beautiful contributions to the theory of Shimura varieties and special values of L-functions. It will highlight cutting edge work on topics such as the construction of Euler systems; relations between special cycles on Shimura varieties and L-functions, such as generalized Gross-Zagier formulas and the Tate conjecture; the construction of Galois representations in cohomology; and related aspects of the theory of automorphic forms.

## April 2023

### Density Problems in Arithmetics

ag.algebraic-geometry nt.number-theory
2023-04-03 through 2023-04-07
Centre International de Rencontres Mathématiques
Luminy; France

Meeting Type: conference

Contact: see conference website

### Description

ln this workshop, we will consider variants of Artin's primitive root conjecture leading to the study of the Galois groups of various radical extensions. Beyond the case of the multiplicative group studied by Lenstra and others, there are now also interesting results for elliptic radicals, and for division points in more general abelian varieties. ln this context, the elliptic analogue of Artin's conjecture is the Lang-Trotter conjecture, which is still open after more than 40 years.

The Galois representations associated to various division points in abelian varieties are central to understanding the Galois groups of the radical extensions that one tries to explicitly describe in this context, as they control the behaviour of the primes in the underlying problems. Understanding these Galois representations, and the entanglement between the extensions generated by different prime-power radicals, is essential to progress in this area.

ln this circle of problems and questions, one encounters interesting restrictions to local-global principles that will be addressed in this workshop, not only in the context of radical extensions.

### Degeneracy of algebraic points

ag.algebraic-geometry nt.number-theory
2023-04-17 through 2023-04-21
MSRI
Berkeley, CA; USA

Meeting Type: conference

Contact: see conference website

### Description

A central topic in Diophantine Geometry is to understand how the geometry of a variety influences the arithmetic of its algebraic points, and conversely. Conjectures of Bombieri, Lang, and Vojta suggest that rational points of algebraic varieties satisfying suitable approximation conditions, are algebraically degenerate. On the other hand, conjectures on unlikely intersections suggest that algebraic points of special type —e.g. torsion points in semi-abelian varieties, special points in Shimura varieties— avoid subvarieties, unless the subvariety itself is also special (in a technical sense).

In recent years, a number of techniques have led to outstanding progress on Lang-Vojta conjectures, such as the Subspace Theorem, p-adic approaches to finiteness, and modular methods. Similarly, spectacular progress has been achieved on unlikely intersection conjectures thanks to new methods and tools, such as height formulas for special points, connections to model theory, refined counting results, and new theorems of Ax-Shanuel type (bi-algebraic geometry).

The goal of this workshop is to create the opportunity for these two groups to interact, to share their techniques, to update on the most recent progress, and to attack the outstanding open questions in the field.

The two directions described above are rather technical and specialized, and it seems necessary to bring together these groups of researchers to explain to each other not only the latest developments in their fields, but also the methods that made possible these breakthroughs. Thus, in this workshop we expect to have lectures explaining the main methods, as well as talks presenting the most recent progress in the subject by the world leading experts.

## May 2023

### The Arithmetic of the Langlands Program

ag.algebraic-geometry nt.number-theory rt.representation-theory
2023-05-02 through 2023-08-18
Bonn; Germany

Meeting Type: thematic program

Contact: see conference website

### Description

The Langlands program aims to relate systems of polynomial equations with integer coefficients to automorphic forms, i.e. functions on symmetric spaces with a large number of discrete symmetries. The focus of the trimester will be on some manifestations of this program, including:

moduli spaces of shtukas
p-adic techniques in local Langlands and the relation to geometric Langlands
Shimura varieties and more general spaces in global Langlands


### Spring school in Arithmetic Statistics

ag.algebraic-geometry nt.number-theory
2023-05-08 through 2023-05-12
Centre International de Rencontres Mathématiques
Luminy; France

Contact: see conference website

### Description

The spring school serves an introduction to the conference "Arithmetic Statistics", and aims to provide PhD students and early stage researchers with the necessary background to enable them to fruitfully partake in the conference. lt will also be an occasion for Master students to have an introduction towards research in number theory.

Along with lecture courses, there will be exercise sessions and a possibility to work on small research projects under the guidance of the lecturers and the researchers proposing them.

The lecture courses will take place in the mornings, while exercise sessions will take place in the afternoon, with extra time allotted for round tables and work in groups.

Lecture courses thematics are the following:

• Galois representations and Diophantine equations,
• Complex Multiplication,
• Class field theory,
• Zeta functions and L-functions,
• Abelian varieties.

### Summer School on the Arithmetic of the Langlands Program

ag.algebraic-geometry nt.number-theory rt.representation-theory
2023-05-08 through 2023-05-12
Hausdorff Research Institute for Mathematics
Bonn; Germany

Contact: see conference website

### Description

This school provides an introduction to some of the main topics of the trimester program. It is mainly directed at PhD students and junior researchers.

### Arithmetic Statistics

ag.algebraic-geometry nt.number-theory
2023-05-15 through 2023-05-19
Centre International de Rencontres Mathématiques
Lumin; France

Meeting Type: conference

Contact: see conference website

### Description

The theme of the conference is a type of number theory that has become very popular over the last decades, and that is influenced by the possibility of « experimentally » studying arithmetic objects with the help of a computer. Thanks to the wide availability of computer algebra systems, essentially any number theorist nowadays has this possibility at his fingertips. There are concrete objects that are not so easily determined « by hand », such as fundamental units in number fields of higher degree, or Mordell-Weil generators of point groups of elliptic curves, and a first impression of « what these typically look like » is often obtained by numerical experimentation.

Over the years, substantial datasets relating to number fields, elliptic curves and L-series have become available, enhancing our understanding of the arithmetic world somewhat beyond only the smallest examples, which may fail to show the true asymptotic behaviour.

### An Expedition into Arithmetic Geometry

ag.algebraic-geometry nt.number-theory
2023-05-30 through 2023-06-02
Leiden; Netherlands

Meeting Type: Conference

Contact: Peter Bruin, Ronald van Luijk, Gabor Wiese

### Description

Conference dedicated to the memory of Bas Edixhoven

## June 2023

### Conference on Local Langlands and p-adic methods

ag.algebraic-geometry nt.number-theory rt.representation-theory
2023-06-12 through 2023-06-16
Hausdorff Research Institute for Mathematics
Bonn; Germany

Meeting Type: conference

Contact: see conference website

### Description

This conference will be on various aspects of the local Langlands correspondence over p-adic fields and methods from p-adic Hodge theory. Topics will include the usual local Langlands correspondence, the p-adic local Langlands correspondence and the relation to coherent sheaves on spaces of Galois representations, and the geometry and cohomology of local Shimura varieties.

### Complex analysis and geometry: celebrating the 70+1th birthday of Laszlo Lempert

ag.algebraic-geometry cv.complex-variables dg.differential-geometry
2023-06-26 through 2023-06-30
Alfred Renyi Institute
Budapest; Hungary

Meeting Type: conference

Contact: Tamas Darvas

### Description

We are going to organize a week long conference during June 26-30, 2023, hosted by the Alfred Renyi Institute of Mathematics in Budapest, Hungary. The topic of the conference will emphasize the rich interactions between complex analysis and complex geometry, within the context of geometric analysis.

In addition, the conference will serve as an opportunity to celebrate the 70+1th birthday of Laszlo Lempert.

## July 2023

### LuCaNT: LMFDB, Computation, and Number Theory

ag.algebraic-geometry nt.number-theory
2023-07-10 through 2023-07-14
ICERM
Providence, RI; USA

Meeting Type: conference

Contact: Andrew V. Sutherland

### Description

This will be a one week conference broadly focused on the topics of the LMFDB, mathematical databases, computation, number theory, and arithmetic geometry. The conference will include invited talks, presentations by authors of papers submitted to the conference and selected by the scientific committee following peer-review, as well as time set aside for research and collaboration. We plan to publish a proceedings volume that will include all of the accepted papers.

### Rational Points 2023

ag.algebraic-geometry nt.number-theory
2023-07-23 through 2023-07-29
Schney/Lichtenfels, Bavaria ; Germany

Meeting Type: workshop

Contact: Michael Stoll

### Description

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.

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.

## August 2023

### Global Langlands, Shimura varieties, and shtukas

ag.algebraic-geometry nt.number-theory rt.representation-theory
2023-08-07 through 2023-08-11
Hausdorff Research Institute for Mathematics
Bonn; Germany

Meeting Type: conference

Contact: see conference website

### Description

This conference will be on various aspects of the global Langlands correspondence. Topics will include in particular the geometry and cohomology of Shimura varieties and more general locally symmetric spaces, or moduli spaces of shtukas.

## September 2023

### Special year on p-adic arithmetic geometry

ag.algebraic-geometry nt.number-theory
2023-09-01 through 2024-04-30