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Upcoming Meetings

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September 2023

Special year on p-adic arithmetic geometry

ag.algebraic-geometry nt.number-theory
2023-09-01 through 2024-04-30
Institute for Advanced Study
Princeton, NJ; USA

Meeting Type: conference

Contact: see conference website

Description

During the 2023-24 academic year the School will have a special program on the p -adic arithmetic geometry, organized by Jacob Lurie and Bhargav Bhatt, who will be the Distinguished Visiting Professor.

The last decade has witnessed some remarkable foundational advances in p-adic arithmetic geometry (e.g., the creation of perfectoid geometry and the ensuing reorganization of p-adic Hodge theory). These advances have already led to breakthroughs in multiple different areas of mathematics (e.g., significant progress in the Langlands program and the resolution of multiple long-standing conjectures in commutative algebra), have uncovered new phenomena that merit further investigation (e.g., the discovery of new structures on algebraic K-theory, new period spaces in p-adic analytic geometry, and new bounds on torsion in singular cohomology), and have made hitherto inaccessible terrains more habitable (e.g., birational geometry in mixed characteristic). This special year intends to bring together a mix of people interested in various facets of the subject, with an eye towards sharing ideas and questions across fields.

December 2023

Lectures on selected areas in Pure Mathematics

ag.algebraic-geometry nt.number-theory
2023-12-21 through 2024-12-31
Institute of Mathematics, VAST, Hanoi, Vietnam
Hanoi ; Vietnam

Meeting Type: lecture

Contact: Phung Ho Hai, Doan Trung Cuong

Description

The purpose of this lecture series is to introduce the audience to basic ideas of specific areas of contemporary pure mathematics. Each lecture shall present an area: where it comes from, where it currently is, where it goes. Lectures will be given by prominent mathematicians twice a year: in the Spring and in the Autumn. Before and after each lecture we will organize reading seminars to prepare the audience for the lecture and to dig further into the topic of the lecture. With the lecturer’s consent, lectures will be recorded, slides and/or lecture notes will be provided if available.

February 2024

Southern California Number Theory Day

nt.number-theory
2024-02-24 through 2024-02-24
University of California San Diego
San Diego, CA; USA

Meeting Type: conference

Contact: see conference website

Description

none

A panorama of moduli spaces

ag.algebraic-geometry co.combinatorics gt.geometric-topology nt.number-theory
2024-02-26 through 2024-03-01
Goethe University Frankfurt
Frankfurt am Main; Germany

Meeting Type: conference

Contact: Martin Ulirsch

Description

none

March 2024

Arizona Winter School 2024: Abelian Varieties

ag.algebraic-geometry nt.number-theory
2024-03-02 through 2024-03-06
University of Arizona
Tucson, AZ; USA

Meeting Type: school for graduate students

Contact: see conference website

Description

Courses:

 Valentijn Karemaker: TBA
 Ben Moonen: TBA
 Rachel Pries: TBA
 Joe Silverman: TBA

With Clay lecturer Barry Mazur

PLANT - Pittsburgh Links among Analysis and Number Theory

ca.classical-analysis-and-odes nt.number-theory
2024-03-04 through 2024-03-07
University of Pittsburgh and Carnegie Mellon University
Pittsburgh, PA; USA

Meeting Type: conference

Contact: Theresa Anderson, Armin Schikorra, Carl Wang-Erickson

Description

The purpose of the conference is to bring together representatives of two disciplines with multiple points of interface: number theory and analysis.

Workshop on p-adic Arithmetic Geometry

ag.algebraic-geometry at.algebraic-topology nt.number-theory
2024-03-11 through 2024-03-15
Institute for Advanced Study
Princeton, NJ; USA

Meeting Type: conference

Contact: see conference website

Description

none

Workshop on Number Theory in Function Fields

nt.number-theory
2024-03-12 through 2024-03-13
Penn State University
University Park, PA; USA

Meeting Type: workshop

Contact: Yen-Tsung Chen

Description

This workshop will bring together senior and early-career mathematicians working in function field field arithmetic with the goal of discussing some of the recent development in theory of Drinfeld modules, t-motives and related topics. The workshop will be two full days. One of the goals of the workshop is to give the opportunity to junior mathematicians to present their research and form new collaborative connections.

Degree d points on algebraic surfaces

ag.algebraic-geometry nt.number-theory
2024-03-18 through 2024-03-22
American Institute of Mathematics
Pasadena, CA; USA

Meeting Type: conference

Contact: see conference website

Description

This workshop, sponsored by AIM and the NSF, will be devoted to the study of degree d points on algebraic surfaces over a number field.

The study of degree d points on algebraic curves over ℚ is a rich and mature area of research, with the Abel-Jacobi map and the Mordell-Lang conjecture providing powerful tools for exploration. However, for higher dimensional varieties there is no such approach that works in general. Because of this, we lack even a conjectural framework for understanding which higher dimensional varieties over ℚ should have "many" degree d points.

The workshop will focus on questions aimed at addressing this dearth, concentrating on the case of algebraic surfaces. For instance, what does it mean for a surface over ℚ to have "many" degree d points? What are some geometric constructions that give rise to abundant degree d points? Are these related to geometric measures of irrationality? If HilbdX has a Zariski dense set of ℚ-points for some small d, does that yield any arithmetic or geometric consequences for X? If X embeds into its Albanese, can we obtain results analogous to that of curves?

Participants will be researchers from a broad array of backgrounds (e.g., arithmetic of surfaces, geometry of Hilbert schemes of surfaces, geometric measures of irrationality, arithmetic of 0-cycles, to name a few), ideally with a curiosity and interest in arithmetic questions.

This event will be run as an AIM-style workshop. 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.

Arithmetic Quantum Field Theory Conference

at.algebraic-topology mp.mathematical-physics nt.number-theory rt.representation-theory
2024-03-25 through 2024-03-29
CMSA
Cambridge, MA; USA

Meeting Type: conference

Contact: David Ben-Zvi, Solomon Friedberg, Natalie Paquette, Brian Williams

Description

The object of the program is to develop and disseminate exciting new connections emerging between quantum field theory and algebraic number theory, and in particular between the fundamental invariants of each: partition functions and L-functions.

On one hand, there has been tremendous progress in the past decade in our understanding of the algebraic structures underlying quantum field theory as expressed in terms of the geometry and topology of low-dimensional manifolds, both on the level of states (via the Atiyah-Segal / Baez-Dolan / Lurie formalism of extended, functorial field theory) and on the level of observables (via the Beilinson–Drinfeld / Costello–Gwilliam formalism of factorization algebras). On the other hand, Weil’s Rosetta Stone and the Mazur–Morishita–Kapranov–Reznikov arithmetic topology (the “knots and primes” dictionary) provide a sturdy bridge between the topology of 2- and 3-manifolds and the arithmetic of number fields. Thus, one can now port over quantum field theoretic ideas to number theory, as first proposed by Minhyong Kim with his arithmetic counterpart of Chern-Simons theory. Most recently, the work of Ben-Zvi–Sakellaridis–Venkatesh applies an understanding of the Langlands program as an arithmetic avatar of electric-magnetic duality in four-dimensional gauge theory to reveal a hidden quantum mechanical nature of the theory of $L$-functions.

The program will bring together a wide range of mathematicians and physicists working on adjacent areas to explore the emerging notion of arithmetic quantum field theory as a tool to bring quantum physics to bear on questions of interest for the theory of automorphic forms, harmonic analysis and L-functions. Conversely, we will explore potential geometric and physical consequences of arithmetic ideas, for example, the Langlands correspondence theory of L-functions for 3-manifolds.

April 2024

Moduli Spaces and Modular Forms

ag.algebraic-geometry nt.number-theory
2024-04-14 through 2024-04-19
Schiermonnikoog; Netherlands

Meeting Type: conference

Contact: see conference website

Description

none

Women in Number Theory and Geometry (WINGs) 2024

ag.algebraic-geometry dg.differential-geometry nt.number-theory sg.symplectic-geometry
2024-04-15 through 2024-04-18
Shrewsbury; UK

Meeting Type: conference

Contact: Isabel Rendell

Description

WINGs 2024 is the fourth instalment of an annual retreat for women, and other underrepresented genders, in number theory and geometry. It is aimed at early career mathematicians, from PhD onwards. Events will include talks from our eight keynote speakers, a career panel which will also feature participants from industry, social activities, to encourage interaction between participants, and short talks, so that participants can learn about each other’s research interests. Our aim is to counteract the isolation which can be experienced by women and other underrepresented genders in mathematics during their career by fostering a sense of community from the start.

The eighth mini simposium of the Roman Number Theory Association

nt.number-theory
2024-04-17 through 2024-04-19
Università
Rome; Italy

Meeting Type: conference

Contact: Valerio Talamanca

Description

This is the eighth edition of the annual mini simposio of the Roman Number Theory Association, Invited speakers include

  • Ramla Abdellatif, Université de Picardie Jules Verne

  • Margaret Bilu, Université de Bordeaux
  • Stephanie Chan, Institute of Science and Technology Austria

  • Francesc Fite, Universitat de Barcelona

  • Andrew Granville, Université de Montréal

  • Mattias Jonsson, University of Michigan

  • Samuel Le Fourn, Université Grenoble Les Alpes
  • Aaron Levin, Michigan State University

  • Jared Duker Lichtman, Stanford University

  • Davide Lombardo, Università di Pisa

  • Laura Paladino, Università della Calabria

  • Sarah Peluse, University of Michigan

  • John Voight, Dartmouth College

  • Jan Vonk, Universiteit Leiden

Arithmetic Geometry - A Conference in Honor of Hélène ESNAULT on the Occasion of Her 70th Birthday

ag.algebraic-geometry nt.number-theory
2024-04-22 through 2024-04-26
IHES
Bures-sur-Yvette; France

Meeting Type: conference

Contact: Elisabeth Jasserand

Description

This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations.

May 2024

Local Systems in Algebraic Geometry

ag.algebraic-geometry nt.number-theory
2024-05-07 through 2024-05-10
The Ohio State University
Columbus, OH; USA

Meeting Type: instructional workshop

Contact: see conference website

Description

none

International Conference on L-functions and Automorphic Forms

nt.number-theory rt.representation-theory
2024-05-13 through 2024-05-16
Vanderbilt University
Nashville, TN; USA

Meeting Type: conference

Contact: see conference website

Description

This conference is devoted to the areas of L-functions and autmorphic forms. In particular, it focusses on the interactions between both fields, which have a long and fruitful history since the fundamental work by Hecke about 90 years ago. The topics will focus on new developments around the areas indicated in the title, as well as establishing and furthering dialogue on new developments at the boundary of these areas. Given the ubiquity of automorphic forms throughout number theory as well as their strong interaction with the field of L-functions, it is very reasonable to expect that both areas will benefit from each other in the future as well. It is likely that this would lead to ideas more broadly useful in other areas of pure mathematics as well as to new types of objects to inspect and new structural questions within both fields.

The Ceresa Cycle in Arithmetic and Geometry

ag.algebraic-geometry nt.number-theory
2024-05-13 through 2024-05-17
ICERM
Providence, RI; USA

Meeting Type: conference

Contact: see conference website

Description

In the 1980s, Ceresa exhibited one of the first naturally occurring examples of an algebraic cycle, the Ceresa cycle, that is in general homologically trivial but algebraically nontrivial. In the last few years, there has been a renewed interest in the Ceresa cycle, and other cycle classes associated to curves over arithmetically interesting fields, and their interactions with analytic, combinatorial, and arithmetic properties of those curves. We hope to capitalize on this momentum to bring together different communities of arithmetic geometers to fully explore explicit computations around the arithmetic and geometry of cycles, when these various approaches are systematically combined.

36th Annual Workshop on Automorphic Forms and Related Topics

nt.number-theory
2024-05-20 through 2024-05-24
Oklahoma State University
Stillwater, OK; USA

Meeting Type: conference

Contact: see conference website

Description

none

June 2024

Visions in Arithmetic and Beyond: Celebrating Peter Sarnak's Work and Impact

ag.algebraic-geometry nt.number-theory
2024-06-03 through 2024-06-07
Princeton University/Institute for Advanced Study
Princeton, NJ; USA

Meeting Type: conference

Contact: see conference website

Description

none

Summer School and Workshop on Relative Langlands Duality

nt.number-theory rt.representation-theory
2024-06-03 through 2024-06-08
University of Minnesota
Minneapolis, MN; USA

Meeting Type: summer school and conference

Contact: see conference website

Description

The relative Langlands program is a generalization of the classical Langlands program from reductive groups to certain homogeneous spaces. The recent work of Ben-Zvi, Sakellaridis, and Venkatesh on relative Langlands duality reveals new connections of the program to algebraic geometry and physics. The summer school and workshop will cover several aspects of the relative Langlands program and explore those new connections.

Dynamical days in Montreal

ds.dynamical-systems nt.number-theory
2024-06-05 through 2024-06-07
Concordia University
Montreal, Quebec; Canada

Meeting Type: Workshop

Contact: Carlo Pagano

Description

This will be a 3-days workshop on arithmetic dynamics. For more information, please see the webpage.

Additive Combinatorics Summer School

co.combinatorics nt.number-theory rt.representation-theory
2024-06-10 through 2024-06-14
Erdős Center of the Alfréd Rényi Institute of Mathematics
Budapest; Hungary

Meeting Type: summer school

Contact: Gergely Kiss, Mate Matolcsi, Gabor Somlai

Description

The summer school is dedicated to graduate students and young researchers, and aims to give an introduction to recent techniques and topics of additive combinatorics. The lectures of the summer school will concentrate on recent developments of the polynomial method, some combinatorial methods of additive combinatorics, and the introduction of Fourier analytic techniques connected to them. The main topics will be presented by top researchers of the area.

The lecturers will be Julia Wolf, Christian Elsholtz, Peter Pal Pach, Sean Prendiville.

Canadian Number Theory Association XVI

nt.number-theory
2024-06-10 through 2024-06-14
Fields Institute
Toronto, ON; Canada

Meeting Type: conference

Contact: see conference website

Description

none

International Conference on Lie Algebra and Number Theory

nt.number-theory ra.rings-and-algebras rt.representation-theory
2024-06-10 through 2024-06-14
National Institute of Technology Calicut
Kozhikode, Kerala; India

Meeting Type: conference

Contact: Dr. Saudamini Nayak, Dr. Chiranjit Ray, Dr. Sudhansu Sekhar Rout

Description

Lie algebras and superalgebras are among the most important algebraic structures with ample applications in modern mathematics like geometry, harmonic analysis, algebra and representation theory, and number theory. Number Theory is one of the oldest and classical branch of mathematics. This conference aims to bring together researchers working in various areas of algebra and number theory to exchange knowledge and further possible collaborations. The key topics of the conference are as follows:

  • Structure and representation theory of finite and infinite dimensional Lie algebras/Lie superalgebras
  • Number Theory (Algebraic Number Theory/ Modular Forms/ Automorphic Forms/ Diophantine Equations/ Partition Theory)
  • Applications of Lie Theory to Number Theory.

CTNT 2024

nt.number-theory
2024-06-10 through 2024-06-16
University of Connecticut
Storrs, CT; USA

Meeting Type: Summer school and conference

Contact: Alvaro Lozano Robledo, Keith Conrad

Description

A summer school during June 10-13, 2024 for advanced undergraduates and beginning graduate students and a conference on arithmetic geometry, number theory, and related topics during June 14-16, 2024.

Additive Combinatorics Workshop

co.combinatorics nt.number-theory rt.representation-theory
2024-06-17 through 2024-06-21
Erdős Center of the Alfréd Rényi Institute of Mathematics
Budapest; Hungary

Meeting Type: conference

Contact: Gergely Kiss, Mate Matolcsi, Gabor Somlai

Description

This conference is devoted to the most recent results of Additive Combinatorics. The topic of the conference is aimed to emphasize the rich interactions between additive combinatorics, harmonic analysis and number theory. The conference will bring together some recognized experts of the field, junior researchers (postdoctoral fellows and graduate students), and senior researchers from various aspects of the main topic. Beside the discussion on the recent progress in the field, it is also aimed to initiate interaction and collaboration among the participants.

Curves, Abelian VArieties, and RElated Topics

ag.algebraic-geometry nt.number-theory
2024-06-17 through 2024-06-21
Universitat de Barcelona
Barcelona, Catalonia; Spain

Meeting Type: conference

Contact: See conference website

Description

See conference website

Modular Forms, L-functions, and Eigenvarieties: a conference in memoriam of Joël Bellaïche

nt.number-theory
2024-06-18 through 2024-06-21
Paris; France

Meeting Type: conference

Contact: see conference website

Description

none

Spec(Q¯(2πi))

ag.algebraic-geometry ca.classical-analysis-and-odes nt.number-theory
2024-06-18 through 2024-06-21
Fields Institute
Toronto, ON; Canada

Meeting Type: conference

Contact: see conference website

Description

After the success and impact of Spec(Q⎯⎯⎯⎯), held at the Fields Institute in 2022, Spec(Q¯(2πi)) again aims to celebrate and promote research advances of LGBTQ2I (Lesbian, Gay, Bisexual, Transgender, Queer, 2-spirit , Intersex) mathematicians specialising in algebraic geometry, arithmetic geometry, commutative algebra, and number theory. The first edition of the conference proved to be extremely important to lay the foundations for a fertile, supportive and stimulating scientific queer community in the areas of algebraic geometry, commutative algebra and number theory. Building on the strengths of the first edition, Spec(Q¯(2πi)) will create an empowering and engaging environment which provides LGBTQ2I visibility in algebraic geometry, will support junior LGBTQ2I 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 topics in 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¯(2πi)) will be aimed at a general algebro-geometric audience.

Conference on Solvable Lattice Models, Number Theory and Combinatorics

co.combinatorics mp.mathematical-physics nt.number-theory
2024-06-24 through 2024-06-26
Trinity College Dubliin
Dublin; Ireland

Meeting Type: conference

Contact: Ben Brubaker, Daniel Bump, Solomon Friedberg, Henrik P.A. Gustafsson, Katrin Wendland

Description

This conference focuses on new and emerging connections between solvable lattice models and special functions on p-adic groups and covering groups, uses of quantum groups, Hecke algebras and other methods to study representations of p-adic groups and their covers, and advances in algebraic combinatorics and algebraic geometry.

Conference on Solvable Lattice Models, Number Theory and Combinatorics

co.combinatorics mp.mathematical-physics nt.number-theory rt.representation-theory
2024-06-24 through 2024-06-26
Hamilton Mathematics Institute, Trinity College Dublin
Dublin; Ireland

Meeting Type: conference

Contact: Solomon Friedberg, Ben Brubaker, Daniel Bump, Henrik Gustafsson, Katrin Wendland

Description

This conference focuses on new and emerging connections between solvable lattice models and special functions on p-adic groups and covering groups, uses of quantum groups, Hecke algebras and other methods to study representations of p-adic groups and their covers, and advances in algebraic combinatorics and algebraic geometry.

Number Theory and Physics

mp.mathematical-physics nt.number-theory
2024-06-24 through 2024-06-28
International Centre for Theoretical Physics
Trieste; Italy

Meeting Type: conference

Contact: see conference website

Description

This workshop aims to bring together experts in number theory and physics, especially on topics on the interface of the two subjects.

Recent Progress on Hilbert’s 12th Problem

ag.algebraic-geometry nt.number-theory
2024-06-24 through 2024-06-28
International Centre for Mathematical Sciences
Edinburgh; UK

Meeting Type: conference

Contact: see conference website

Description

Hilbert’s twelfth problem asks for explicit constructions of the abelian extensions of a given number field, similar to what is known for the rational numbers and for imaginary quadratic fields. These abelian extensions are known as class fields because their Galois groups are identified with certain generalized ideal class groups. In the two known cases, the class fields are obtained via the adjunction of roots of unity and of torsion points on elliptic curves with complex multiplication. These are special values of complex analytic functions – the exponential function and elliptic functions with complex multiplication. Hilbert may have envisioned the use of special values of complex analytic functions to construct class fields of more general base fields.

In the 1970s, Harold Stark proposed a strikingly original approach to the generation of class fields, based on his conjectures on the leading term of Artin L-functions at s = 0 [St75]. In the case of abelian L-functions with a simple zero at s = 0, Stark predicted that the first derivative was the logarithm of a unit in the respective class field [St76], so exponentiating this derivative would give a generator for the abelian extension. In the two known cases, this reduced to the theory of circular and elliptic units, thanks to Dirichlet’s analytic class number formula and Kronecker’s limit formula. Although there is now extensive computational evidence that Stark’s conjecture is correct, there has been little progress on its solution.

In the 1980s Benedict Gross formulated some p-adic [Gr82] and tame [Gr88] analogues of Stark’s conjectures, which gave more information on the p-adic expansions of the conjectural units. Since the p adic L-functions involved in Gross’s conjecture are related to certain Galois modules via the main conjecture in Iwasawa theory, these conjectures have proved more amenable than their complex analogs. Refinements of the Gross-Stark conjecture were proposed in [DD06], and the p-adic conjectures of [Gr82] was proved in [DDP11]. This line of argument has culminated in the recent work of Samit Dasgupta and Mahesh Kakde [DKa], [DKb] which, by proving a large part of the conjectures of [Gr88] (along with the refinement [DD06] of the conjectures of [Gr82] in the broader setting of totally real fields) leads to a p−adic solution to Hilbert’s twelfth problem for this large class of fields.

The goal of this workshop is to take stock of this striking recent development and of other progress around the theme of related approaches to explicit class field theory. The key to much of the progress over the years is the careful study of p-adic and tame deformations of modular forms, most notably, of Hilbert modular Eisenstein series. The p-adic interpolation of classical Eisenstein series was introduced by Jean-Pierre Serre [Se72] to study the congruences of special values of L-functions and the construction of p-adic L-functions for totally real fields, and was further developed by Barry Mazur and Andrew Wiles in their proof of the main conjecture of Iwasawa theory [MW84]. The workshop will focus on the breakthroughs in [DKa] and [DKb], with a lecture series by the two authors forming the cornerstone of the activity.

July 2024

Arithmetic Geometry and Applications

ag.algebraic-geometry nt.number-theory
2024-07-01 through 2024-07-05
Trieste; Italy

Meeting Type: conference

Contact: see conference website

Description

none

p-adic Families of Automorphic Forms: Theories and Applications

ag.algebraic-geometry nt.number-theory
2024-07-08 through 2024-07-12
International Centre for Mathematical Sciences
Edinburgh; UK

Meeting Type: conference

Contact: see conference website

Description

The idea of p-adic families of automorphic forms grew out of work of Serre and Swinnerton-Dyer in the 70s exploring congruences between the q-expansion coefficients of modular forms. Work of Hida, Coleman and Mazur made the investigation of p-adic families one of the central topics in the arithmetic of modular forms. In the following decades there were striking applications to the construction of p-adic L-functions, Iwasawa theory and modularity of Galois representations.

One powerful organising principle has been to parametrize p-adic modular forms (or, more generally, p-adic automorphic forms) by p-adic analytic spaces known as eigenvarieties (or eigencurves, in the one-dimensional case originally considered by Coleman and Mazur). Our understanding of the geometry of eigenvarieties and their relationship to moduli spaces of Galois representations has rapidly developed, but there are still many important open questions.

An overarching objective of this meeting will be to bring together people working on the different theories of p-adic automorphic forms and various applications (or potential applications). We hope that this will inspire new collaborations and insights.

The Mordell conjecture 100 years later

ag.algebraic-geometry nt.number-theory
2024-07-08 through 2024-07-12
MIT
Cambridge, MA; USA

Meeting Type: conference

Contact: Jennifer Balakrishnan, Philipp Habegger, Bjorn Poonen, Andrew V. Sutherland, Wei Zhang

Description

none

Uniformity and Stability of Oscillatory Integrals

nt.number-theory
2024-07-08 through 2024-07-12
Hausdorff Center for Mathematics
Bonn; Germany

Meeting Type: summer school

Contact: see conference website

Description

Because of the ubiquity of Fourier analysis, oscillatory integrals are present in many techniques in both harmonic analysis and analytic number theory. Current state-of-the-art methods in both fields are pushing beyond classical methods because of increased importance of understanding the uniformity and stability of the estimates. In addition, researchers are uncovering unifying ideas that span the (traditionally somewhat separated areas) of oscillatory integrals in the setting of analysis, and character sums in number theory. Recent work on estimating oscillatory integrals have even applied model theory, from logic.

This summer school will give participants an introduction on the classical methods for estimating oscillatory integrals and explain current cutting-edge developments. Throughout, the lectures will view these problems through a lens of understanding the uniformity and stability of the estimates.

Arithmetic Geometry

ag.algebraic-geometry nt.number-theory
2024-07-14 through 2024-07-19
Mathematische Forschungsinstitut Oberwolfach
Oberwolfach; Germany

Meeting Type: conference

Contact: see conference website

Description

none

Sixteenth Algorithmic Number Theory Symposium (ANTS XVI)

nt.number-theory
2024-07-15 through 2024-07-19
Massachusetts Institute of Technology
Cambridge, Massachusetts; USA

Meeting Type: conference

Contact: Jennifer Balakrishnan, Andrew Sutherland, John Voight

Description

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

August 2024

The Third JNT Biennial Conference in Number Theory

nt.number-theory
2024-08-20 through 2024-08-26
Scuola Normale Superiore de Pisa
Cetraro; Italy

Meeting Type: conference

Contact: DORIAN GOLDFELD

Description

The Journal of Number Theory hosts a number theory conference every two years to publicize recent advances in the field. The JNT also sponsors the David Goss Prize, a 10K USD prize awarded every two years to a young researcher in number theory and presented at the JNT Biennial.

Analytic Number Theory and Arithmetic Statistics

ag.algebraic-geometry nt.number-theory
2024-08-26 through 2024-08-30
Centre de recherches mathématiques
Montréal, QC; Canada

Meeting Type: conference

Contact: see conference website

Description

none

September 2024

Explicit methods in number theory

nt.number-theory
2024-09-01 through 2024-09-07
Mathematisches Forschungsinstitut Oberwolfach
Oberwolfach; Germany

Meeting Type: workshop

Contact: Karim Belabas, Bjorn Poonen, Fernando Rodriguez Villegas

Description

The aim of this meeting is to bring together people attacking key problems in number theory via techniques involving concrete or computable descriptions. Here, number theory is interpreted broadly, including algebraic and analytic number theory, Galois theory and inverse Galois problems, arithmetic of curves and higher-dimensional varieties, zeta and L-functions and their special values, and modular forms and functions. Considerable attention is paid to computational issues, but the emphasis is on aspects that are of interest to the pure mathematician.

Because of limited space, participation is by invitation only.

Algebraic Number Theory - A workshop for young researchers

nt.number-theory
2024-09-02 through 2024-09-06
Universität der Bundeswehr München
Munich, Bavaria; Germany

Meeting Type: conference

Contact: Ben Forrás, Sören Kleine, Justina Lückehe, Katharina Müller, Andreas Nickel, Johannes Sprang

Description

The workshop is primarily aimed at researchers on the doctoral and early postdoctoral level. Besides some already announced mini-courses and research talks, we will offer selected participants the opportunity to present their own work.

Number Theory in the Americas 2

nt.number-theory
2024-09-08 through 2024-09-13
Casa Matemática Oaxaca (CMO)
Oaxaca; Mexico

Meeting Type: collaborative research workshop

Contact: see conference website

Description

In 2019, the organizers created a workshop called Number Theory in the Americas, which brought together junior and senior mathematicians from North, Central, and South America, to work together on research projects. The workshop resulted in at least seven publications, and served as a first collaboration experience for many of the junior researchers. The organizers propose to create a follow-up workshop in order to provide collaboration opportunities for the PhD students and postdocs who were too young to participate the last time. The workshop will be held in Spanish in order to erase the additional obstacle of communicating in English. We will welcome native and non-native speakers alike.

Our workshop is modeled after several other workshops that have been successful at fostering mathematical collaboration. Participants will be divided into small project groups (3-5 participants) containing a mix of junior and senior researchers. Each group will be led by one or two senior mathematicians. Project groups will be assigned based on research area, with care taken to ensure that each group contains researchers from both continents who have not previously worked together. Background reading will be sent to project group members several months in advance so that they are prepared to work on their respective problems together when they arrive in Oaxaca. The bulk of the workshop will be devoted to working in the project groups, but there will be introductory talks on the first day and final reports on the last day. There will also be panel discussions on topics of particular interest to junior researchers. The expectation is not that each project group will write a paper by the end of the week. Rather, it is meant to be an opportunity to exchange ideas and a starting point for potential future collaboration.

Ramification in geometric Langlands and non-abelian Hodge theory

ag.algebraic-geometry nt.number-theory rt.representation-theory
2024-09-09 through 2024-09-13
Heidelberg University
Heidelberg, Baden-Württemberg; Germany

Meeting Type: workshop

Contact: Andreas Hohl, Johannes Horn, Konstantin Jakob, Judith Ludwig, Timo Richarz

Description

This workshop is motivated by recent developments in geometric representation theory, related to wild ramification in the geometric Langlands program and non-abelian Hodge theory. The goal is to bring together researchers in these fields and researchers working on irregular singularities (in particular Stokes phenomena), to stimulate future interactions.

It will feature research talks from experts in the field, a poster session for early-career researchers as well as three mini-courses by

Jean-Baptiste Teyssier (Sorbonne Université), Valerio Toledano-Laredo (Northeastern University) and Zhiwei Yun (Massachusetts Institute of Technology).

Introduction to Number Theory and Algebraic Curves

nt.number-theory
2024-09-09 through 2024-09-20
Mathematical Institute SASA and Faculty of Mathematics, University of Belgrade
Belgrade; Serbia

Meeting Type: Summer school

Contact: see conference website

Description

CIMPA/AESIM introductory school of number theory for developing countries

November 2024

p-adic geometry

ag.algebraic-geometry nt.number-theory
2024-11-18 through 2024-11-22
National University of Singapore
Singapore; Singapore

Meeting Type: instructional workshop

Contact: see conference website

Description

none

December 2024

Representations of p-adic Groups - application form for early career researchers

rt.representation-theory nt.number-theory
2024-12-01 through 2024-12-06
Mathematisches Forschungsinstitut Oberwolfach
Oberwolfach; Germany

Meeting Type: conference

Contact: Jessica Fintzen, David Schwein, Maarten Solleveld

Description

See the website for details on the subject matter of the workshop.

Per MFO rules, participation is generally limited to invited mathematicians. However, we have reserved a small number of places for early-career mathematicians, who may apply to participate by completing a short application.

May 2025

NUMBER THEORY, QUANTUM CHAOS AND THEIR INTERFACES A conference in honor of Zeev Rudnick's 64 birthday

mp.mathematical-physics nt.number-theory
2025-05-18 through 2025-05-22
Tel Aviv University
Tel Aviv; Israel

Meeting Type: conference

Contact: see conference website

Description

The conference "Number Theory, Quantum Chaos and their Interfaces” aims at gathering distinguished researchers working in either of the disciplines to discuss recent research advances in these fields, and serve as a playground for the exchange of ideas between these, rather diverse, research communities. Another purpose of our conference is to provide a solid educational platform for more junior researchers who aspire to conduct research in the relevant fields and expose them to some of the outstanding results and open problems.

June 2025

Algebraic Points on Curves

ag.algebraic-geometry nt.number-theory
2025-06-23 through 2025-06-27
ICERM
Providence, RI; USA

Meeting Type: conference

Contact: see conference website

Description

In recent years, there has been an explosion of activity surrounding algebraic points on curves, from many different perspectives. These include the study of measures of irrationality, isolated and parametrized points, computational methods to determine algebraic points, and the arithmetic statistics of algebraic points. In this workshop, we aim to bring together researchers from these diverse perspectives, with the particular goal of developing bridges between them. The workshop will include overview talks on the various perspectives, research talks, an open problem session, and structured time for collaboration.

Journées Arithmétiques

nt.number-theory
2025-06-30 through 2025-07-04
University of Luxembourg
Luxembourg; Luxembourg

Meeting Type: conference

Contact: see conference website

Description

none

July 2025

LMFDB, Computation, and Number Theory (LuCaNT 2025)

nt.number-theory
2025-07-07 through 2025-07-11
Institute for Computational and Experimental Research in Mathematics (ICERM)
Providence, RI; USA

Meeting Type: conference

Contact: Andrew Sutherland

Description

none

August 2025

René 25

ag.algebraic-geometry nt.number-theory
2025-08-18 through 2025-08-22
University of French Polynesia
Punaauia; French Polynesia

Meeting Type: conference

Contact: see conference website

Description

The René 25 conference's purpose is to celebrate the research interests of René Schoof.

September 2025

Special Year on Arithmetic Geometry, Hodge Theory, and O-minimality

lo.logic ag.algebraic-geometry nt.number-theory
2025-09-01 through 2026-04-30
Institute for Advanced Study
Princeton, NJ; USA

Meeting Type: conference

Contact: see conference website

Description

During the 2025-26 academic year the School will have a special program on Arithmetic Geometry, Hodge Theory, and O-minimality. Jacob Tsimerman, University of Toronto will be the Distinguished Visiting Professor.

The purpose of this special year will focus on recent developments in hodge theory and o-minimality and their applications to arithmetic geometry. There has been much progress over the last 15 years in using transcendental uniformization maps to study arithmetic questions (general shafarevich theorems, results on unlikely intersections, general bounds on rational point counts). It has become increasingly clear that hodge theory (both classical and P-adic) and the resulting period maps form a natural home for these kinds of investigations to arise. In the other direction, O-minimality has been applied with success to make progress on questions in Hodge theory (Griffiths conjecture, definable period maps), and has recently had its own explosion of results (sharply O-minimal sets, the resolution of Wilkie's conjecture).

The goal of this year will be to bring together researchers in these different fields, with the aim of extending the collaboration between areas, share key insights, and investigate how far existing methods can be pushed.

Senior participants: Gal Binaymini, Ben Bakker (to be confirmed), Jonathan Pila and Claire Voisin (STV)