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Upcoming Meetings

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September 2021

Six functors formalism and Motivic homotopy theory

ag.algebraic-geometry at.algebraic-topology
2021-09-19 through 2021-09-24
University of Milano
Milano; Italy

Meeting Type: Summer school and conference

Contact: Fabrizio Andreatta, Federico Binda, Alberto Vezzani, Paul Arne Østvaer

Description

“Six functors formalism and Motivic homotopy theory”

Milano, September 20-24, 2021 Department of Mathematics “F. Enriques”, University of Milano, Milan, Italy.

Sponsored by the University of Milan and the Research Council of Norway within the project “Equations in motivic homotopy”.

The school will include three-mini courses for PhD students and young postdocs:

Minicourses:

  • Alberto Canonaco (Pavia)
  • Frédéric Déglise (ENS Lyon)
  • Martin Gallauer (Oxford)

In addition to research talks by

  • Mattia Cavicchi (Strasbourg)
  • Alberto Merici (Zurich)
  • Mattia Ornaghi (Be'er Sheva)
  • Sabrina Pauli (Duisburg-Essen)
  • Charanya Ravi (Regensburg)
  • Timo Richarz (Darmstadt)
  • Florian Strunk (Regensburg)

Funding for participants is available. Deadline for financial support is July 10th, 2021.

Number theory Down Under 9

nt.number-theory
2021-09-27 through 2021-09-30
The University of Sydney
Sydney; Australia

Meeting Type: conference

Contact: see conference website

Description

This is the ninth conference "Number Theory Down Under", a major annual number theoretic event in Australia.

Unifying themes in geometry

ag.algebraic-geometry nt.number-theory
2021-09-27 through 2021-09-30
Lake Como School of Advanced Studies
Como; Italy

Meeting Type: conference

Contact: see conference website

Description

none

"Cyclic Cohomology at 40: achievements and future prospects"

ag.algebraic-geometry at.algebraic-topology ct.category-theory dg.differential-geometry ds.dynamical-systems fa.functional-analysis kt.k-theory-and-homology mp.mathematical-physics nt.number-theory oa.operator-algebras qa.quantum-algebra ra.rings-and-algebras rt.representation-theory
2021-09-27 through 2021-10-01
Fields Institute
Toronto/Ontario; Canada

Meeting Type: conference

Contact: Katia Consani

Description

The forthcoming Conference “Cyclic Cohomology at 40: achievements and future prospects” will take place online at The Fields Institute, from September 27 to October 1st 2021:

Registration instructions are here:

http://www.fields.utoronto.ca/activities/21-22/cyclic-cohomology

Representation theory's hidden motives

ag.algebraic-geometry rt.representation-theory
2021-09-27 through 2021-10-01
University of Münster and University of Sydney
Münster and Sydney; Germany

Meeting Type: conference

Contact: Jakob Scholbach

Description

In recent years, motivic techniques have been applied in several branches of representation theory, for example in geometric and modular representation theory. The goal of this workshop is to bring together researchers in these areas in order to foster new synergies in topics such as foundational aspects of the theory of motives, Tate motives on varieties of representation-theoretic origin, motivic aspects of the Langlands program, and motives of classifying spaces.

October 2021

Oregon Number Theory Days

nt.number-theory
2021-10-02 through 2021-10-02
Portland State University
Portland, OR; USA

Meeting Type: seminar day

Contact: Derek Garton

Description

A triannual number theory seminar rotating between Oregon State University, Portland State University, and the University of Oregon.

Lattices and Cohomology of Arithmetic Groups: Geometric and Computational Viewpoints

gr.group-theory gt.geometric-topology nt.number-theory
2021-10-03 through 2021-10-08
Banff International Research Station
Banff, AB; Canada

Meeting Type: conference

Contact: see conference website

Description

A lattice is a discrete collection of regularly ordered points in space. Lattices are everywhere around us, from the patterned stacked arrangements of fruits and vegetables at the grocery to the regular networks of atoms in crystalline compounds. Today lattices find applications throughout mathematics and the sciences, applications ranging from chemistry to cryptography and Wi-Fi networks.

The focus of this meeting is the connections between lattices and number theory and geometry. Number theory, one of the oldest branches of pure mathematics, is devoted to the study properties of the integers and more sophisticated number systems. Lattices and number theory have many deep connections. For instance using number theory it was recently demonstrated that certain packings of balls in high dimensions are optimally efficient. Lattices also appear naturally when one studies certain spaces that play an important role in number theory; one of the main focuses of this meeting is to investigate computational and theoretical methods to understand such spaces and to expand the frontier of our algorithmic knowledge in working with them.

Cohomology of Arithmetic Groups: Duality, Stability, and Computations

gr.group-theory gt.geometric-topology nt.number-theory
2021-10-10 through 2021-10-15
Banff International Research Station
Banff, AB; Canada

Meeting Type: conference

Contact: see conference website

Description

The cohomology of arithmetic groups is the study of the properties of ``holes'' in geometric spaces that contain information about number theory. The workshop will bring together mathematicians with expertise in number theory, topology, and geometric group theory to tackle these problems and explore recent developments.

Upstate Number Theory Conference

nt.number-theory
2021-10-23 through 2021-10-24
Union College
Schenectady, NY; USA

Meeting Type: conference

Contact: Jeffrey Hatley

Description

The Tenth Annual Upstate Number Theory Conference will take place Saturday, October 23 & Sunday, October 24, 2021, in-person on the campus of Union College in Schenectady, NY.

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

November 2021

The Maple Conference 2021

ac.commutative-algebra ag.algebraic-geometry co.combinatorics ct.category-theory dg.differential-geometry fa.functional-analysis gm.general-mathematics gr.group-theory
2021-11-02 through 2021-11-05
Maplesoft
Waterloo, Ontario; Canada

Meeting Type: Free virtual conference

Contact: Jennifer Iorgulescu

Description

The Maple Conference 2021 - Maple in Mathematics Education and Research

This FREE virtual conference is dedicated to exploring different aspects of the math software Maple, including Maple's impact on education, new symbolic computation algorithms and techniques, and the wide range of Maple applications. Attendees will have the opportunity to learn about the latest research, share experiences, and interact with Maple developers.

The conference will take place online, and will include live presentations and discussions as well as recordings and chatrooms, in order to accommodate time zones. Maplesoft staff will also offer Maple training sessions on a variety of topics during the conference.

All presenters at the conference are invited to submit a full paper. These submissions undergo peer-review, and the decision about acceptance or rejection lies with the Program Committee. Accepted papers are published in the conference proceedings.

January 2022

Higher Algebraic Structures In Algebra, Topology And Geometry

ag.algebraic-geometry at.algebraic-topology gt.geometric-topology kt.k-theory-and-homology sg.symplectic-geometry
2022-01-10 through 2022-04-29
Institute Mittag-Leffler
Djursholm; Sweden

Meeting Type: research program

Contact: Gregory Arone, Tilman Bauer, Alexander Berglund, Søren Galatius, Jesper Grodal, Thomas Kragh

Description

We are happy to announce that the Institut Mittag-Leffler will be hosting a research program entitled

"HIGHER ALGEBRAIC STRUCTURES IN ALGEBRA, TOPOLOGY AND GEOMETRY”

from January 10, 2022 to April 29, 2022.

Junior researchers (advanced PhD students or young postdocs) can apply for a fellowship to attend the program, covering all expenses (deadline: December 31, 2020). For all others, the program is by invitation only.

Institut Mittag-Leffler in Danderyd, just north of Stockholm, Sweden, is an international centre for research and postdoctoral training in mathematical sciences. The oldest mathematical research institute in the world, it was founded in 1916 by Professor Gösta Mittag-Leffler and his wife Signe, who donated their magnificent villa, with its first-class library, for the purpose of creating the institute that bears their name.

Program web page: http://www.mittag-leffler.se/langa-program/higher-algebraic-structures-algebra-topology-and-geometry

Junior research fellowships: http://www.mittag-leffler.se/research-programs/junior-fellowship-program

The organizers
Gregory Arone ([email protected])
Tilman Bauer ([email protected])
Alexander Berglund ([email protected])
Søren Galatius ([email protected])
Jesper Grodal ([email protected])
Thomas Kragh ([email protected])

March 2022

Automorphic Forms Beyond GL_2

ag.algebraic-geometry nt.number-theory rt.representation-theory
2022-03-05 through 2022-03-09
University of Arizona
Tucson, AZ; USA

Meeting Type: conference

Contact: see conference website

Description

none

Rational Points 2022

ag.algebraic-geometry nt.number-theory
2022-03-27 through 2022-04-02
Frankenakademie Schloss Schney
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.

April 2022

Periods, motives and differential equations: between arithmetic and geometry, on the occasion of Yves André's 60th++ birthday

ag.algebraic-geometry nt.number-theory
2022-04-11 through 2022-04-15
IHP
Paris; France

Meeting Type: conference

Contact: see conference website

Description

Periods occur in various branches of mathematics and as the title of our conference indicates, their study intertwines arithmetic, Diophantine analysis, differential equations, and algebraic geometry. Many interesting results have been proved in recent years and many challenging problems on periods are still open. The aim of our conference is to bring together specialists who cover all these different points of view and their ramifications, with special attention towards possible applications to broader areas of the techniques developed in the study of periods and their realizations.

Yves André has contributed in many ways to this ongoing adventure and this conference will not only be the opportunity to listen to a broad range of recent developments in mathematics around the topic of periods, but also to celebrate his 60th birthday.

Rational points on higher-dimensional varieties

ag.algebraic-geometry nt.number-theory
2022-04-25 through 2022-04-29
ICMS
Edinburgh; UK

Meeting Type: conference

Contact: Daniel Loughran, Rachel Newton, Efthymios Sofos

Description

The meeting will not be online.

Speakers include: Francesca Balestrieri, Jen Berg, Tim Browning, Yang Cao, Jean-Louis Colliot-Thélène, Jordan Ellenberg, Roger Heath-Brown, Marta Pieropan, Bjorn Poonen, Damaris Schindler, Alexei Skorobogatov, Olivier Wittenberg.

Details: The topic of rational points on varieties over the rational numbers is the modern perspective on the theory of Diophantine equations.

There is a good (partially conjectural) understanding now of the situation for algebraic curves. The proof of the Mordell conjecture for curves of genus at least 2 by Faltings is one of the crowning achievements in the area, and much of the work on elliptic curves is driven by the Birch-Swinnerton-Dyer conjecture. Recent highlights include the work of Bhargava and his collaborators on average ranks of elliptic curves. The situation in higher dimensions is much murkier however.

The aim of the meeting is to bring together leading experts and early career researchers to make progress on understanding rational points on surfaces and higher dimensional varieties. Traditionally there have been two separate communities working in the area, using tools from analytic number theory and algebraic geometry, respectively. Spectacular progress has been made in recent times by managing to bridge these communities, with a particular highlight being applications of Green-Tao-Ziegler's work on primes in arithmetic progressions to the fibration method. The emphasis in the meeting will be on building upon this bridge and further inspiring collaboration between the analytic and geometric communities.

Specific topics to be covered will include the following:

Schinzel's Hypothesis with probability Campana points. Purity of strong approximation. Rational points in families. Brauer--Manin obstruction.

May 2022

Leuca2022 Celebrating Claude Levesque's Damien Roy's and Michel Waldschmidt's birthdays

nt.number-theory
2022-05-16 through 2022-05-21
Marina di San Gregorio, Patù (Lecce), Italy; Italy

Meeting Type: conference

Contact: Valerio Talamanca

Description

none

La grandezza dei punti piccoli Celebrating Francesco Amoroso's 60th birthday

nt.number-theory
2022-05-23 through 2022-05-25
Universita' di Pisa
PISA; Italy

Meeting Type: conference

Contact: Valerio Talamanca

Description

none

Franco-Asian Summer School on Arithmetic Geometry in Luminy

ag.algebraic-geometry nt.number-theory
2022-05-30 through 2022-06-03
Centre International de Rencontres Mathématiques (CIRM)
Luminy - Marseille; France

Meeting Type: summer school

Contact: Ahmed Abbes

Description

The Franco-Asian summer school on arithmetic geometry is a continuation of the many fruitful joint France-Asia events that have taken place since the Asian Year on Motives initiated by Jean-Marc Fontaine at IHES in 2006. These collaborations have had a considerable impact on the international development of fundamental branches of arithmetic geometry. This new event, organized at CIRM, will be open to students and young researchers from all over the world. It will consist in four mini-courses and several lectures.

Pre-registration on the web is mandatory for all participants who wish to attend the summer school in person at CIRM. The number of participants is limited to 90. Please complete the pre-registration form here:

http://www.cirm-math.fr/preRegistration/index.php?EX=menu0&id_renc=2534

June 2022

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
Toronto, Ontario; Canada

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

The success of modern codes for large-scale optimization is heavily dependent on the use of effective tools of numerical linear algebra. On the other hand, many problems in numerical linear algebra lead to linear, nonlinear or semidefinite optimization problems. The purpose of the conference is to bring together researchers from both communities and to find and communicate points and topics of common interest. This Conference has been organised in cooperation with the Society for Industrial and Applied Mathematics (SIAM). Conference topics include any subject that could be of interest to both communities, such as: • Direct and iterative methods for large sparse linear systems. • Eigenvalue computation and optimization. • Large-scale nonlinear and semidefinite programming. • Effect of round-off errors, stopping criteria, embedded iterative procedures. • Optimization issues for matrix polynomials • Fast matrix computations. • Compressed/sparse sensing • PDE-constrained optimization • Distributed computing and optimization • Applications and real time optimization Invited Speakers Invited Speakers to be confirmed shortly. Registration Registration is currently open at 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. Call for Papers and Mini-Symposiums Mini-symposium proposals and contributed talks are invited on all aspects of numerical linear algebra and optimization. Mini-symposium proposals should be submitted to [email protected] by 31 January 2022. A mini-symposium consists of up to four speakers. For emerging topics the mini-symposium can be extended to at most two sessions on a single topic (maximum eight speakers). Organisers will be advised of acceptance by 14 February 2022. Contributed talks and mini-symposia talks will be accepted on the basis of a one page extended abstract which should be submitted by 28 February 2020 online at http://online.ima.org.uk/ or by e-mail to [email protected] Authors will be advised of acceptance by 31 March 2022. A book of abstracts will be made available to delegates at the conference. Key deadlines Mini-symposia proposals: 31 January 2022 Notification of acceptance of mini-symposia: 14 February 2022 Abstract submission: 28 February 2022 Notification of acceptance of abstracts: 31 March 2022 Authors will be advised of acceptance by 31 March 2022. A book of abstracts will be made available to delegates at the conference.

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

Spec$(\overline{Q})$

ac.commutative-algebra ag.algebraic-geometry nt.number-theory
2022-07-06 through 2022-07-08
Fields Institute
Toronto, ON; Canada

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.

Park City Mathematics Institute: Number theory informed by computation

nt.number-theory
2022-07-17 through 2022-08-06
IAS/PCMI
Park City, UT; USA

Meeting Type: conference and summer school

Contact: Bjorn Poonen

Description

none

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

Women in Numbers Europe - 4

nt.number-theory
2022-08-29 through 2022-09-02
Utrecht University
Utrecht; Netherlands

Meeting Type: workshop

Contact: Ramla Abdellatif, Valentijn Karemaker, Ariane Mézard

Description

This is a workshop that aims to support new collaborations for women in number theory. Prior to the conference, the project leaders will design projects and provide background reading and references for their groups. Each participant will be assigned to a working group according to her research interests. During the workshop there will be some talks and career-development activities, but there will also be ample time dedicated to working in the working groups.

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.

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

Description

none

Around p-adic cohomologies

ag.algebraic-geometry nt.number-theory
2022-09-19 through 2022-09-23
University of Padova
Padova; Italy

Meeting Type: conference

Contact: see conference website

Description

none

October 2022

Conference on Arithmetic Algebraic Geometry

ag.algebraic-geometry nt.number-theory
2022-10-03 through 2022-10-07
TU Darmstadt
Darmstadt; Germany

Meeting Type: conference

Contact: Ulrich Görtz

Description

none

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

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

Description

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.

March 2023

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.

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

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.

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.