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Upcoming Meetings

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April 2019

Reinventing Rational Points

ag.algebraic-geometry nt.number-theory
2019-04-15 through 2019-07-12
Institut Henri Poincare
Paris; France

Meeting Type: thematic program

Contact: see conference website

Description

Rational points on algebraic varieties represent a modern way of thinking about one of the oldest problems in mathematics: integral and rational solutions of Diophantine equations. In arithmetic geometry one views rational points in the context of geometric properties of underlying algebraic varieties. In analytic number theory many different analytic techniques are used to count the number of rational or integral points, and so understand their “average” behaviour. In logic, rational points feature prominently in the work on Hilbert’s Tenth Problem over Q, which asks for an algorithm to decide the existence of rational solutions to all Diophantine equations. Here one searches for examples of “weird” or “far from average” behaviour of rational points.

There is a large body of conjectures that describe the behaviour of rational points. They include various versions of Mazur’s conjectures on the real topological closure of the set of rational points. A related circle of conjectures deals with the Brauer–Manin obstruction designed to describe the closure of the set of rational points inside the topological space of adelic points. It is conjectured that the Brauer–Manin obstruction should exactly describe this closure for certain classes of algebraic varieties such as rationally connected varieties, K3 surfaces and algebraic curves. Supportive heuristic and theoretical evidence for these difficult conjectures is slowly emerging from the work of many people. The Batyrev–Manin conjectures on the growth of rational points of bounded height have received much attention by analytic number theorists. New techniques that have revolutionised analytic number theory, such as additive combinatorics (Green, Tao, Ziegler) or arithmetic invariant theory (Bhargava, Gross), have made it possible to solve some of the long standing problems in arithmetic geometry. A new feature in recent years has been an increased interaction between the analytic and geometric thinking: questions motivated by various counting problems give rise to novel geometric ideas, whereas conjectures coming from geometry open up new fields of investigation for analytic number theorists.

The aim of this thematic period is to bring together senior and junior mathematicians from the various domains related to rational points to foster new interactions and new research.

May 2019

INdAM special research activity in Padova on "p-adic Langlands program"

nt.number-theory
2019-05-12 through 2019-07-12
Università degli Studi di Padova
Padova; Italy

Meeting Type: Special research bimester

Contact: see conference website

Description

none

July 2019

Algebraic Geometry, Number Theory and Applications in Cryptography and Robot kinematics

ag.algebraic-geometry nt.number-theory
2019-07-02 through 2019-07-13
AIMS Cameroon, CIMPA,
Limbe, South West Region; Cameroon

Meeting Type: conference

Contact: see conference website

Description

The CIMPA School offers an intensive teaching session to graduate students and young researchers in the fields of Algebraic Geometry, Number Theory, Applications in Cryptography and Robot kinematics. This course will provide elements needed for the applications in cryptography and robot kinematics which will be developed at the end of the school. The goal of this course is for every participant to be able to select a suitable hyperelliptic curve $C$ for constructing some cryptosystems based on the discrete logarithm problem in its Jacobian $J_C$.

European Talbot Workshop 2019: Algebraic K-theory

ag.algebraic-geometry at.algebraic-topology ct.category-theory kt.k-theory-and-homology
2019-07-07 through 2019-07-13
Rheinböllen; Germany

Meeting Type: Workshop

Contact: Bertram Arnold, Luci Bonatto, Jack Davies, Alice Hedenlund

Description

The fifth European Talbot workshop will take place in Germany July 7 - 13, 2019. The goal is to bring together a group of 30-35 graduate students and post-docs to work on a focused topic, this year algebraic K-theory, under the guidance of two senior mentors.

Most of the talks were given by the participants, with enough free time in the afternoon and evenings for further discussions and interaction. The character of the workshop is expository in nature, starting with the basic ideas and leading to a survey of the most recent developments in the field. Since all participants are staying together at a group house, jointly responsible for cooking and cleaning, we hope to create an informal and inspiring atmosphere.

Perfectoids

ag.algebraic-geometry nt.number-theory
2019-07-08 through 2019-07-12
Henri Lebesgue Center for Mathematics
Rennes; France

Meeting Type: summer school, conference

Contact: see conference website

Description

An international summer school and conference on perfectoid spaces will take place July 8–12, 2019 in Rennes. The first part of the week, until the Thursday morning, will feature courses by international specialists on perfectoid rings, adic spaces and perfectoid spaces. From Thursday afternoon until the end of the conference invited speakers will present their latest results in the field. Participants and lecturers are generally expected to be present the entire week, but they also have the possibility to attend only the research conference on Thursday and Friday.

Periods and motives

nt.number-theory ag.algebraic-geometry
2019-07-08 through 2019-07-12
Humboldt University
Berlin; Germany

Meeting Type: conference

Contact: see conference website

Description

none

SIAM Conference on Applied Algebraic Geometry

ag.algebraic-geometry
2019-07-09 through 2019-07-13
University of Bern
Bern; Switzerland

Meeting Type: conference

Contact: see conference website

Description

none

Rational Points 2019

ag.algebraic-geometry nt.number-theory
2019-07-14 through 2019-07-20
Schloss Schney; Germany

Meeting Type: conference

Contact: see conference website

Description

none

Arithmetic of Connections

ag.algebraic-geometry ca.classical-analysis-and-odes nt.number-theory
2019-07-15 through 2019-07-19
ETH, Zurich
Zurich; Switzerland

Meeting Type: summer school

Contact: see conference website

Description

The summer school will revolve around arithmetic aspects of the theory of differential equations. This topic, which can be traced back at least to Gauss's study of hypergeometric functions, was a major driving force of mathematical research in the 19th century. It witnessed a spectacular revival during the next century thanks to the interaction with several seemingly unrelated areas of mathematics, in particular algebraic geometry (Higgs bundles and Simpson’s conjecture), and number theory (Siegel-Shidlovskii Theorem and transcendence theory).

p-adic modular forms and Galois representations

ag.algebraic-geometry nt.number-theory
2019-07-15 through 2019-07-19
The University of Sheffield
Sheffield ; UK

Meeting Type: conference

Contact: Tobias Berger, Betina Adel

Description

A five day conference at the University of Sheffield focusing on several topics in arithmetic geometry: Shimura Varieties, p-adic Galois representations, p-adic families of automorphic forms, p-adic Hodge theory and eigenvarieties.

Recent advances in the arithmetic of Galois representations

nt.number-theory
2019-07-15 through 2019-07-19
Dipartimento di Matematica, Università degli Studi di Genova
Genova; Italy

Meeting Type: conference

Contact: Matteo Longo, Stefano Vigni

Description

none

The First Journal of Number Theory Biennial Conference

nt.number-theory
2019-07-26 through 2019-07-29
Journal of Number Theory and Scuola Normale Superiore
Cetraro; Italy

Meeting Type: conference

Contact: See conference website

Description

The Journal of Number Theory will host a number theory conference every two years to publicize recent advances in the field. The JNT is sponsoring the David Goss Prize of 10K USD to be awarded every two years at the JNT Biennial to a young researcher in number theory. Proceedings of the JNT Biennial conferences will appear in a special volume of the JNT.

Equivariant Topology and Derived Algebra, in honour of John Greenlees’s 60th birthday

ag.algebraic-geometry at.algebraic-topology ac.commutative-algebra
2019-07-29 through 2019-08-02
NTNU
Trondheim; Norway

Meeting Type: conference

Contact: Scott Balchin, David Barnes, Magdalena Kedziorek, Markus Szymik, Gareth Williams

Description

A Jolly Pleasant Conference for Greenlees (J.P.C. Greenlees) officially known as Equivariant Topology and Derived Algebra

A conference in honour of John’s 60th birthday

Geometric methods in p-adic representation theory

nt.number-theory rt.representation-theory
2019-07-29 through 2019-08-02
Mathematical Institute, University of Oxford
Dublin; Ireland

Meeting Type: conference

Contact: Konstantin Ardakov, Peter Schneider

Description

The goal of this workshop is to bring together researchers who work in number theory or representation theory or non-archimedean analysis, with an eye towards recent developments in the p-adic representation theory of p-adic groups.

Among others, the themes of the workshop include:

  • applications to the p-adic local Langlands program,
  • constructing representations through the cohomology of Drinfeld coverings,
  • p-adic analogues of Beilinson-Bernstein localisation,
  • techniques from differential-graded categories.

WARTHOG 2019: Foundations of Tropical Geometry

ag.algebraic-geometry co.combinatorics
2019-07-29 through 2019-08-02
University of Oregon
Eugene, OR; USA

Meeting Type: summer school

Contact: Ben Elias

Description

The workshop is intended for graduate students with some postdocs, and will be led by Diane Maclagan and Jeff Giansiracusa. More information can be found on the workshop webpage.

Young Researchers' Workshop on non-Archimedean and tropical geometry

ag.algebraic-geometry
2019-07-29 through 2019-08-02
Universitaet Regensburg
Regensburg; Germany

Meeting Type: conference

Contact: Philipp Jell, Helene Sigloch, Martino Stoffel, Veronika Wanner

Description

The follow-up to the 2015 and 2017 Students' Conferences on tropical and non-Archimedean geometry will take place in July/August 2019 in Regensburg. The target audience are PhD students and young postdocs.

Our workshop will consist of three introductory talks to tropical and non-Archimedean geometry. For the rest of the week, the participants have the opportunity to give talks about their research. We encourage everyone to apply for giving a talk by submitting an abstract.

We can offer funding, especially for PhD and Masters students. We plan on funding housing and travel expenses for all speakers plus some more participants.

August 2019

Arithmetic and Algebraic Geometry

ag.algebraic-geometry nt.number-theory
2019-08-05 through 2019-08-09
University of Michigan, Ann Arbor
Ann Arbor, Michigan; USA

Meeting Type: conference

Contact: Bhargav Bhatt, Evangelia Gazaki

Description

none

Number Theory in the Americas

nt.number-theory
2019-08-11 through 2019-08-16
Casa Matemática Oaxaca
Oaxaca; Mexico

Meeting Type: collaboration conference

Contact: see conference website

Description

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

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

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

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

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

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

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

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

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

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

Arithmetic Geometry and Quantum Field Theory

ag.algebraic-geometry mp.mathematical-physics nt.number-theory
2019-08-12 through 2019-08-16
Korea Institute for Advanced Study
Seoul; South Korea

Meeting Type: conference

Contact: see conference website

Description

This workshop continues the investigation of the interface between number theory, geometry, and physics started in last year’s workshop. Some of the themes covered include Hodge theory and physics, arithmetic of black holes, mirror symmetry, arithmetic of scattering amplitudes, arithmetic gauge theories, and modularity of BPS states. The number of physicists around the world interested in number theory seems to be steadily increasing as are the number of activities. Over the past year, the organiser MK has spoken at the mathematical physics seminar in Heidelberg, the mathematics and physics colloquium in Amsterdam, and two Simons conferences on string theory and number theory. The current activity at KIAS attempts to present a coherent view of many of the most recent developments and insights for the benefit of participants and speakers.

Graduate Summer School on the Geometry and Modular Representation Theory of Algebraic Groups

ag.algebraic-geometry rt.representation-theory
2019-08-19 through 2019-08-23
Simons Center for Geometry and Physics
Stony Brook, NY; USA

Meeting Type: Graduate Summer School

Contact: Mark Andrea de Cataldo, Francois Greer, Christian Schnell

Description

The goal of this summer school is to introduce Ph.D. students and Postdocs to exciting recent developments in the geometry of algebraic groups and in modular representation theory.

The school will consist of two morning lecture series and of afternoon lectures on topics directly related to the morning lecture series.

Michel Brion (Grenoble) will give one lecture series on the “Structure of algebraic groups and geometric applications”. Geordie Williamson (Sydney) will give the other lecture series “On the modular representation theory of algebraic groups.”

M. Brion’s abstract. The course will first give an overview of the “classical” structure theory of algebraic groups and of some related geometric developments and problems; for example, on automorphism groups of projective algebraic varieties. It will then address results and questions on algebraic groups over arbitrary fields, including the structure of pseudo-reductive groups (work of Conrad, Gabber and Prasad), and of pseudo-abelian varieties (Totaro). Five lectures, 75 minutes each.

G. Williamson’s abstract. This course will be about the modular (i.e. characteristic p) representation theory of reductive algebraic groups, like the general linear and symplectic groups. I will begin by reviewing the algebraic theory, where there are beautiful connections to classical Lie theory and finite group theory. I will then pass to the geometric theory (perverse and parity sheaves) which is behind recent breakthroughs in the subject. The theory is rich in mysteries and open conjectures, and I will try to outline potentially interesting research directions. Five lectures, 75 minutes each.

Structure of Length 3 Resolutions

ac.commutative-algebra ag.algebraic-geometry rt.representation-theory
2019-08-19 through 2019-08-23
University of California, San Diego
San Diego, CA; USA

Meeting Type: conference

Contact: see conference website

Description

A finite free resolution over a commutative local ring is universal for its set of ranks if every other finite free resolution with the same set of ranks can be obtained from it via base change. The existence is formal, however the question remained whether the universal ring can be taken to be noetherian. Hochster established this in 1975 in the length 2 case. Recent advances have connected this story to Kac-Moody Lie algebras and representation theory and the goal of this workshop is to introduce this research area to graduate students, with special emphasis on the length 3 case. The structure of the universal ring controls the structure of free resolutions of a given rank, and this new link allows one to explore this with the use of representation theory.

We have travel and lodging support for students and young researchers. Please use the registration form if you are interested in attending.

The plan is to have 2 introductory lectures each morning (example topics are linkage, structure theorems for finite free resolutions, basic representation theory), with problem sessions and time to write Macaulay2 code in the afternoons. Prior experience with Macaulay2 will be very helpful and participants will be able to work on computer projects with a research component.

Visions of Algebraic Groups

ag.algebraic-geometry gr.group-theory kt.k-theory-and-homology
2019-08-26 through 2019-08-30
Euler International Mathematical Institute (EIMI)
St. Petersburg; Russia

Meeting Type: summer school

Contact: see conference website

Description

none

Women in Numbers Europe 3

ag.algebraic-geometry nt.number-theory
2019-08-26 through 2019-08-30
Henri Lebesgue Center for Mathematics
Rennes; France

Meeting Type: conference

Contact: see conference website

Description

This is a workshop that aims to support new collaborations between female mathematicians. Before the workshop, each participant will be assigned to a working group according to her research interests. Prior to the conference, the project leaders will design projects and provide background reading and references for their groups.

Confirmed group leaders:

Irene Bouw (Ulm)
Rachel Newton (Reading) and Ekin Ozman (Bogazici)
Damaris Schindler (Utrecht) and Lilian Matthiessen (KTH)
Ramla Abdellatif (Picardie Jules Verne)
Cecilia Salgado (Rio de Janeiro)
Elisa Gorla (EPFL)
Eimear Byrne (Dublin) and Relinde Jurrius (Neuchâtel)
Kristin Lauter (Microsoft)
Marcela Hanzer (Zagrev)
Lejla Smajlovic (Sarajevo)

September 2019

24th Central European Number Theory Conference

nt.number-theory
2019-09-01 through 2019-09-06
J. Selye University, Komárno
Komárno; Slovakia

Meeting Type: conference

Contact: Lukáš Novotný

Description

Central European Number Theory Conference (CENT) is the successor of the traditional Czech and Slovak International Conference on Number Theory (NTC) which has been organized since 1972.

p-adic Langlands correspondence: a constructive and algorithmic approach

ag.algebraic-geometry nt.number-theory rt.representation-theory
2019-09-02 through 2019-09-06
Henri Lebesgue Center for Mathematics
Rennes; France

Meeting Type: conference

Contact: see conference website

Description

The aim of arithmetic geometry is to solve equations on integers by geometric methods. One of the most prominent achievements of this approach is certainly the Langlands program, which makes a connection between representations of the absolute Galois group of $\mathbb Q$ and certain adelic representations of reductive algebraic groups. In the early 2000's, Christophe Breuil suggested the existence of a purely $p$-adic version of the Langlands correspondence and supported his vision by numerous examples. Almost twenty years after, the $p$-adic Langlands correspondence has become a major topic in number theory.

Besides, following the rapid development of computer science throughout the 20th century, a large panel of algorithmical tools has been deployed and are now quite performant, in particular for attacking questions in Number Theory. A computational approach to the (classical) Langlands correspondence has been already investigated in recent times as well. We believe that the time has come to begin to extend it to the $p$-adic Langlands correspondence.

This conference is a first step towards this perspective. It will bring together the most internationally recognized experts in $p$-adic Langlands correspondence on the one hand and effective aspects of the Langlands correspondence on the other hand. Young researchers, and more generally researchers who are familiar with one side (either the abstract one or the effective one) and are willing to learn the other side, are particularly encouraged to attend our event: a enthousiastic program with 2 mini-courses, a bunch of short lectures and an introduction to the mathematical software SageMath is specially designed for them.

Petersburg Motives

ag.algebraic-geometry kt.k-theory-and-homology
2019-09-02 through 2019-09-06
Euler International Mathematical Institute (EIMI)
St. Petersburg; Russia

Meeting Type: conference

Contact: see conference website

Description

none

LMFDB as a microscope and a telescope

nt.number-theory ag.algebraic-geometry
2019-09-04 through 2019-09-06
AIM
San Jose, CA; USA

Meeting Type: conference

Contact: see conference website

Description

This workshop, sponsored by AIM, EPSRC, and the NSF, will introduce participants to the L-functions and Modular Forms Database (LMFDB) as a tool for research and teaching.

The LMFDB contains a wealth of information on L-functions, modular forms of several types, elliptic curves and genus 2 curves, number fields, and much more. In addition to detailed information about individual objects, the LMFDB also includes information about connections between objects, including the connections described by the Langlands Program.

The workshop will involve a mixture of demonstrations, explorations, discussions about mathematical content, and discussions about the future of the LMFDB.

Emerging Research in Algebraic Groups, Motives, and K-Theory

ag.algebraic-geometry kt.k-theory-and-homology
2019-09-09 through 2019-09-13
Euler International Mathematical Institute (EIMI)
St. Petersburg; Russia

Meeting Type: conference

Contact: see conference website

Description

none

Emerton-Gee Stack and Related Topics, Hausdorff Summer School

ag.algebraic-geometry nt.number-theory
2019-09-09 through 2019-09-13
Hausdorff Center for Mathematics
Bonn; Germany

Meeting Type: Summer School

Contact: Johannes Anschütz, Arthur-César Le Bras, Andreas Mihatsch

Description

The goal of this school is to give a detailed and example-based introduction, accessible to PhD students and post-docs in the field, to the Emerton-Gee stack: its construction, its properties and some of its applications.

Perfectoid spaces

ag.algebraic-geometry nt.number-theory
2019-09-09 through 2019-09-20
International Centre for Theoretical Sciences
Bengaluru; India

Meeting Type: summer school

Contact: see conference website

Description

In this school, we intend to understand connections between the arithmetic theory of modular forms and new developments in p-adic Hodge theory that grew from the breakthrough work of Peter Scholze on perfectoid spaces (see P. Scholze "Perfectoid spaces" Publ. Math. de l’IHES 116 (2012)).

p-adic methods play a key role in the study of arithmetic properties of modular forms. This theme takes its origins in Ramanujan congruences between the Fourier coeffcients of the unique eigenform of weight 12 and the Eisenstein series of the same weight modulo the numerator of the Bernoulli number B12. After the work of Deligne on Ramanujan's conjecture it became clear that congruences between modular forms reflect deep properties of corresponding p-adic representations. The general framework for the study of congruences between modular forms is provided by the theory of p-adic modular forms developed in fundamental papers of Serre, Katz, Hida and Coleman (1970's-1990's).

p-adic Hodge theory was developed in pioneering papers of Fontaine in 80’s as a theory classifying p-adic representations arising from algebraic varieties over local fields. It culminated with the proofs of Fontaine's de Rham, crystalline and semistable conjectures (Faltings, Fontaine-Messing, Kato, Tsuji, Niziol,...). In order to classify all p-adic representations of Galois groups of local fields, Fontaine (1990) initiated the theory of (φ, Г)-modules. This gave an alternative approach to classical constructions of the p-adic Hodge theory (Cherbonnier, Colmez, Berger). The theory of (φ, Г)-modules plays a fundamental role in Colmez's construction of the p-adic local Langlands correspondence for GL2. On the other hand, in their famous paper on L-functions and Tamagawa numbers, Bloch and Kato (1990) discovered a conjectural relation between p-adic Hodge theory and special values of L-functions. Later Kato discovered that p-adic Hodge theory is a bridge relating Beilinson-Kato Euler systems to special values of L-functions of modular forms and u sed it in his work on Iwasawa-Greenberg Main Conjecture. One expects that Kato’s result is a particular case of a very general phenomenon.

The mentioned above work of Scholze represents the main conceptual progress in p-adic Hodge theory after Fontaine and Faltings. Roughly speaking it can be seen as a wide generalization, in the geometrical context, of the relationship between p-adic representations in characteristic 0 and characteristic p provided by the theory of (φ,Г)-modules. As an application of his theory, Scholze proved the monodromy weight conjecture for toric varieties in the mixed characteristic case. On the other hand, in a series of papers, Scholze applied his theory to the study of the cohomology of Shimura varieties. In particular to the construction of mod p Galois representations predicted by the conjectures of Ash (see P. Scholze “On torsion in the cohomology of locally symmetric space" (Ann. Of Math. 182 (2015)). Another striking application of this theory is the geometrization of the local Langlands correspondence in the mixed characteristic case. Here the theory of Fontaine—Fargues plays a fundamental role.

This goal of the proposed summer school is twofold:

  1. Give an advanced introduction to Scholze's theory.
  2. To understand the relation between perfectoid spaces and some aspects of arithmetic of modular (or, more generally, automorphic) forms such as representations mod p, and lifting of modular forms, completed cohomology, local Langlands program and special values of L-functions.

We wish to bring together experts in the area of arithmetic geometry that will felicitate future research in the direction. We strongly encourage participation of young researchers.

Computations in motivic homotopy theory

ag.algebraic-geometry at.algebraic-topology ct.category-theory kt.k-theory-and-homology
2019-09-16 through 2019-09-20
SFB Higher Invariants, University of Regensburg
Regensburg; Germany

Meeting Type: autumn school

Contact: Denis-Charles Cisinski, Markus Land, Florian Strunk, Georg Tamme

Description

An autumn school on computations in motivic homotopy theory with lecture series by Marc Hoyois, Oliver Röndigs, Kirsten Wickelgren, and Paul Arne Østvær. Please register at the school's website. Limited financial support is available.

Over and around sites in characteristic p

ag.algebraic-geometry nt.number-theory
2019-09-18 through 2019-09-20
Padova; Italy

Meeting Type: conference

Contact: see conference website

Description

We would like to study the definition of sites linked to schemes in finite chararcteristic. In the recent years such a study has merged several techniques: from anaytic spaces to perfectoids to the developing of various p-adic cohomological theories: syntomic, rigid, overcongent ones. We aim to gather in Padova some of the best known experts in the field. It would be also an opportunity to celebrate the legacy of the work of BERNARD LE STUM on all these subjects.

MANTIS: Michigan Algebra and Number Theory Intercity Symposium

nt.number-theory
2019-09-21 through 2019-09-21
University of Michigan
Ann Arbor, MI; USA

Meeting Type: one-day conference

Contact: see conference website

Description

First iteration of a recurring one-day number theory conference, especially targeting faculty and students at nearby universities.

Wild Ramification and Irregular Singularities

ag.algebraic-geometry nt.number-theory
2019-09-23 through 2019-09-27
IM PAN
Warsaw; Poland

Meeting Type: conference

Contact: see conference website

Description

The planned topics include recent advances in ramification of â„“-adic sheaves, study of irregular holonomic D-modules in higher dimensions, irregular Hodge theory, exponential motives, companions, finiteness results for local systems, etc. There are well-known analogies between wild ramification in characteristic p and irregular singularities of meromorphic differential equations, and one of our aims is to bring experts in these and related areas together.

Women in Geometry and Topology

ag.algebraic-geometry at.algebraic-topology ct.category-theory dg.differential-geometry gt.geometric-topology sg.symplectic-geometry
2019-09-25 through 2019-09-27
Centre de Recerca Matemàtica (CRM)
Bellaterra (Barcelona), Catalonia; Spain

Meeting Type: workshop

Contact: Imma Gálvez-Carrillo

Description

he workshop Women in Geometry and Topology is an endeavour organized by the GEOMVAP research group at UPC and financed under the AGAUR project 2017SGR932.

The group GEOMVAP focuses in Geometry and Topology in the broad sense and its applications to several topics suchs as Celestial Mechanics, Control Theory, Mathematical Physics, Phylogenetics and Robotics. GEOMVAP promotes, in particular, Responsible, Research and Innovation within the framework of Horizon 2020. Among the RRI initiatives we strive for gender equality, public engagement, science communication and the visibility of women in Science and Society.

The Workshop Women in Geometry and Topology will feature several plenary talks by top female mathematicians and some contributed talks (contributed by speakers of any gender identity).

There will be two public lectures by Marta Macho (Scientific Culture Chair UPV/EHU, RSME Medal 2015, Emakunde Equality Prize 2016) and Carme Torras (Narcís Monturiol Medal 2000) addressed to the general public (you don't need to be a mathematician to follow them you just need to be curious!). A panel (open to the public) will also be organized in order to discuss the situation of women in mathematics, the gender gap and strategies for breaking the glass-ceiling inside and outside academia. Other complementary activities will be announced in due time.

The publication of "extended abstracts" from the congress is expected in the prestigious Springer-Birkhäuser Research Perspectives CRM Barcelona collection, within the Trends in Mathematics series.

New Developments in Representation Theory of p-adic Groups

nt.number-theory rt.representation-theory
2019-09-29 through 2019-10-05
MFO
Oberwolfach; Germany

Meeting Type: conference

Contact: see conference website

Description

none

October 2019

MAGNTS: Midwest Arithmetic Geometry and Number Theory Series

ag.algebraic-geometry nt.number-theory
2019-10-12 through 2019-10-13
Ohio State University
Columbus, OH; USA

Meeting Type: conference

Contact: Wei Ho, Roman Holowinsky, Jennifer Park, Kevin Tucker

Description

Weekend regional conference in number theory and arithmetic geometry, featuring two mini-courses and additional research lectures.

Automorphic p-adic L-functions and regulators

nt.number-theory
2019-10-14 through 2019-10-18
University of Lille
Lille; France

Meeting Type: conference

Contact: Mladen Dimitrov

Description

The aim of this workshop is to provide an overview of recent developments in theory of p-adic L-functions associated to automorphic representations, covering both the construction of p-adic L-functions, and their relations to Euler systems in Galois cohomology via regulator maps. The workshop will consist of three mini-courses, aimed at younger researchers, and more specialised individual lectures.

There will be three mini-courses, each consisting of four lectures, on the following topics:

Construction of p-adic L-functions for automorphic forms on GL(2n), using the automorphic modular symbols introduced in work of Dimitrov Construction of p-adic L-functions for GSp(4), using Pilloni’s higher Hida theory evalulation of global cohomology classes under the syntomic regulator, using the methods of Darmon—Rotger. The other talks will explore connections of these topics with other related areas of current research, such as Iwasawa theory, the theory of Hecke varieties and the theory of L-invariants.

Modularity and Moduli Spaces

ag.algebraic-geometry nt.number-theory
2019-10-20 through 2019-10-25
Casa Matemática Oaxaca
Oaxaca; Mexico

Meeting Type: conference

Contact: see conference website

Description

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

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

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

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

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

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

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

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

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

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

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

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

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

Oberwolfach Seminar: Topological Cyclic Homology and Arithmetic

at.algebraic-topology kt.k-theory-and-homology nt.number-theory
2019-10-20 through 2019-10-26
Mathematisches Forschungsinstitut Oberwolfach
Oberwolfach; Germany

Meeting Type: week-long meeting with talks by organizers and participants

Contact: Dustin Clausen, Lars Hesselholt, Akhil Mathew

Description

We organize an Oberwolfach Seminar on Topological Cyclic Homology and Arithmetic. The purpose of the seminar is to introduce the higher algebra refinements of determinant and trace, namely, algebraic K-theory and topological cyclic homology, along with their budding applications in arithmetic geometry and number theory. In particular, we will use these ingredients to build Clausen's Artin map from K-theory of locally compact topological R-modules to the dual of his Selmer K-theory of R, and explain that for R a finite, local, or global field, this implies Artin reciprocity. If you wish to participate, please follow the instructions described here to register at ag@mfo.de by August 11, 2019.

Illustrating Number Theory and Algebra

qa.quantum-algebra oa.operator-algebras ag.algebraic-geometry ac.commutative-algebra nt.number-theory ra.rings-and-algebras rt.representation-theory
2019-10-21 through 2019-10-25
ICERM
Providence, RI; USA

Meeting Type: workshop/conference

Contact: Katherine Stange

Description

The symbiotic relationship between the illustration of mathematics and mathematical research is now flowering in algebra and number theory. This workshop aims to both showcase and develop these connections, including the development of new visualization tools for algebra and number theory. Topics are wide-ranging, and include Apollonian circle packings and the illustration of the arithmetic of hyperbolic manifolds more generally, the visual exploration of the statistics of integer sequences, and the illustrative geometry of such objects as Gaussian periods and Fourier coefficients of modular forms. Other topics may include expander graphs, abelian sandpiles, and Diophantine approximation on varieties. We will also focus on diagrammatic algebras and categories such as Khovanov-Lauda-Rouquier algebras, Soergel bimodule categories, spider categories, and foam categories. The ability to visualize complicated relations diagrammatically has led to important advances in representation theory and knot theory in recent years.

Number Theory Series in Los Angeles

nt.number-theory
2019-10-26 through 2019-10-27
Occidental College
Los Angeles, CA ; USA

Meeting Type: conference

Contact: Jim Brown

Description

NTS-LA is a biannual regional number theory theory conference located in Los Angeles. While each meeting with feature two plenary talks by faculty and one plenary talk from a graduate student from outside of Southern California, the majority of talks will consist of 20 minute contributed talks. The purpose of these meetings is to establish a community of people interested in number theory in Southern California, to allow faculty at institutions that do not have funds for regular seminars to attend high-quality research talks, and to provide a friendly environment for students and faculty to present their research.

November 2019

Analytic Number Theory

nt.number-theory
2019-11-03 through 2019-11-09
MFO
Oberwolfach; Germany

Meeting Type: conference

Contact: see conference website

Description

none

p-adic cohomology and arithmetic geometry 2019

nt.number-theory ag.algebraic-geometry
2019-11-11 through 2019-11-15
Tohoku University
Sendai; Japan

Meeting Type: conference

Contact: see conference website

Description

none

December 2019

Rational Points on Higher Dimensional Varieties

ag.algebraic-geometry nt.number-theory
2019-12-02 through 2019-12-06
RIMS Kyoto University
Kyoto; Japan

Meeting Type: conference

Contact: Sho Tanimoto

Description

Visit the conference website for more info.

A2C: Algebra, Codes and Cryptography. International Conference in honor of Prof. Mamadou Sangharé

ac.commutative-algebra ag.algebraic-geometry co.combinatorics it.information-theory ra.rings-and-algebras
2019-12-05 through 2019-12-07
Cheikh Anta Diop University
Dakar; Senegal

Meeting Type: conference

Contact: Laila Mesmoudi

Description

The first Algebra, Codes and Cryptography conference will be held in Dakar, Senegal on Thursday to Saturday, December 5-7, 2019. The conference aims to provide a forum for researchers from all over the world to present results and exchange ideas on topics in Non-Associative Algebra, Non-commutative Algebra, Cryptology, Coding Theory and Information Security.

17th IMA International Conference on Cryptography and Coding

ac.commutative-algebra ag.algebraic-geometry co.combinatorics it.information-theory
2019-12-16 through 2019-12-18
St Anne’s College, University of Oxford
Oxford; UK

Meeting Type: conference

Contact: Conferences Department Institute of Mathematics and its Applications

Description

The mathematical theory and practice of both cryptography and coding underpins the provision of effective security and reliability for data communication, processing and storage. This seventeenth International Conference in an established and successful IMA series on the theme of “Cryptography and Coding” solicits both original research papers and presentations on all technical aspects of cryptography and coding.

January 2020

K-Theory, Algebraic Cycles and Motivic Homotopy Theory

ag.algebraic-geometry mp.mathematical-physics nt.number-theory
2020-01-06 through 2020-06-30
Isaac Newton Institute
Cambridge; UK

Meeting Type: thematic research program

Contact: see conference website

Description

The programme will focus on the areas of Algebraic K-theory, Algebraic Cycles and Motivic Homotopy Theory. These are fields at the heart of studying algebraic varieties from a cohomological point of view, which have applications to several other fields like Arithmetic Geometry, Hodge theory and Mathematical Physics.

It was in the 1960s that Grothendieck first observed that the various cohomology theories for algebraic varieties shared common properties, which led him to explain the underlying kinship of such cohomology theories in terms of a universal motivic cohomology theory of algebraic varieties. The theory of Algebraic Cycles, Higher Algebraic K-theory, and Motivic Homotopy Theory are modern versions of Grothendieck's legacy. In recent years it has seen some spectacular developments, on which we want to build further.

The programme will also specifically explore the connections between the following areas:

Algebraic K-theory, Motivic Cohomology, and Motivic Homotopy Theory;
Hodge theory, Periods, Regulators, and Arithmetic Geometry;
Mathematical Physics.

For this, we shall bring together mathematicians working on different aspects of this broad area for extended periods of time, promoting exchange of ideas and stimulating further progress.

During the programme there will be four workshops. At the very beginning, there will be a workshop aimed at giving a younger generation of mathematicians an overview of and introduction to this interesting, but broad area. Later there will be a workshop for each of the three areas listed above, aimed at the latest developments and applications of that area.

Lattices: Algorithms, Complexity and Cryptography

ag.algebraic-geometry nt.number-theory
2020-01-14 through 2020-05-15
Simons Institute for the Theory of Computing
Berkeley, CA; USA

Meeting Type: thematic program

Contact: see conference website

Description

The study of integer lattices serves as a bridge between number theory and geometry and has for centuries received the attention of illustrious mathematicians including Lagrange, Gauss, Dirichlet, Hermite and Minkowski. In computer science, lattices made a grand appearance in 1982 with the celebrated work of Lenstra, Lenstra and Lovász, who developed the celebrated LLL algorithm to find short vectors in integer lattices. The role of lattices in cryptography has been equally, if not more, revolutionary and dramatic, playing first a destructive role as a potent tool for breaking cryptosystems, and later as a new way to realize powerful and game-changing notions such as fully homomorphic encryption. These exciting developments over the last two decades have taken us on a journey through such diverse areas as quantum computation, learning theory, Fourier analysis and algebraic number theory.

We stand today at a turning point in the study of lattices. The promise of practical lattice-based cryptosystems together with their apparent quantum-resistance is generating a tremendous amount of interest in deploying these schemes at internet scale. However, before lattice cryptography goes live, we need major advances in understanding the hardness of lattice problems that underlie the security of these cryptosystems. Significant, ground-breaking progress on these questions requires a concerted effort by researchers from many different areas: (algebraic) number theory, (quantum) algorithms, optimization, cryptography and coding theory.

The goal of the proposed special semester is to bring together experts in these areas in order to attack some of the main outstanding open questions, and to discover new connections between lattices, computer science, and mathematics. The need to thoroughly understand the computational landscape and cryptographic capabilities of lattice problems is greater now than ever, given the possibility that secure communication on the internet and secure collaboration on the cloud might soon be powered by lattices.

February 2020

A CIMPA research school on Group Actions in Arithmetic and Geometry

nt.number-theory rt.representation-theory
2020-02-17 through 2020-02-28
Gadjah Mada University
Yogyakarta, Indonesia; Indonesia

Meeting Type: Cimpa research school

Contact: Valerio Talamanca

Description

The concept of a group is central to essentially all of modern mathematics. In Number theory and geometry, where groups take central stage in various shapes such as symmetry groups, Galois groups, fundamental groups, reflection groups and permutation groups, the conceptual unification that it provides is most strikingly illustrated. The School will help the students acquiring a good background on the Langlands program, which, after all, is about relations between symmetries in geometry, analysis and number theory. In this school, we present groups and the natural objects they act on in a variety of arithmetic and geometric contexts. Special emphasis will be given to concrete examples, and practical and computational aspects of groups and their actions will be stressed. The topics to be treated include finite fields, coding theory, covering spaces, representation theory, modular forms and Galois theory.

March 2020

Equivariant Stable Homotopy Theory and p-adic Hodge Theory

ag.algebraic-geometry at.algebraic-topology nt.number-theory
2020-03-01 through 2020-03-06
Banff, AB; Canada

Meeting Type: conference

Contact: see conference website

Description

The Banff International Research Station will host the "Equivariant Stable Homotopy Theory and p-adic Hodge Theory" workshop in Banff from March 1 to March 06, 2020.

Algebraic topology has had a long and fruitful collaboration with algebraic geometry, with each providing techniques and problems to the other. This workshop is aimed at an exciting, evolving incarnation of this story: applications of equivariant stable homotopy to number theory. Recent work on the foundations of equivariant stable homotopy theory (starting with the Hill--Hopkins--Ravenel work on the Kervaire invariant one problem) and Lurie's development of the foundations of ''derived algebraic geometry'' now allows systematic exploration and organization of ''equivariant derived algebraic geometry''. This allows us to do ordinary algebraic geometry in commutative ring spectra.

New foundations in this area have been spectacularly applied to phenomena seen in the trace methods approach to computing algebraic K -theory. For instance, although the theory of equivariant commutative ring spectra was described decades ago, few of the subtleties in the theory were understood or explored. The modern approaches to computing algebraic K-groups step through equivariant commutative ring spectra via the natural S1-action on topological Hochschild homology. Ongoing and transformative work by Bhatt--Morrow-Scholze in p-adic Hodge theory uses cyclotomic spectra and therefore subtle equivariant information. This workshop, at the vanguard of work in this area, seeks to bring together experts in algebraic topology, (derived) algebraic geometry, and number theory to explore these exciting new connections.

Higher Dimensional Algebraic Geometry--An event in honor of Prof. Shokurov's 70th Birthday

ag.algebraic-geometry
2020-03-16 through 2020-03-22
Johns Hopkins University
BALTIMORE, Maryland; USA

Meeting Type: conference

Contact: Jingjun Han

Description

Organizing Committee: Caucher Birkar (University of Cambridge), Christopher Hacon (the University of Utah), Chenyang Xu (M.I.T.) with help from Jingjun Han (Johns Hopkins University).

Principal Japanese Organizers: Keiji Oguiso (University of Tokyo), Shunsuke Takagi (University of Tokyo).

This one year long program at Johns Hopkins University will feature 3 graduate-level courses, one conference, three Kempf lectures, three Monroe H. Martin lectures, several colloquiums and weekly seminars.

Tentative schedule for the conference: March 16--22, 2020.

Arithmetic geometry, cycles, Hodge theory, regulators, periods and heights

ag.algebraic-geometry nt.number-theory
2020-03-30 through 2020-04-03
Isaac Newton Institute
Cambridge; UK

Meeting Type: conference

Contact: see conference website

Description

none

April 2020

Periods, Motives and Differential equations: between Arithmetic and Geometry

ag.algebraic-geometry nt.number-theory
2020-04-06 through 2020-04-10
IHP
Paris; France

Meeting Type: conference

Contact: https://periodes.sciencesconf.org/resource/page/id/1

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.

Arithmetic, algebra and algorithms — celebrating the mathematics of Hendrik Lenstra

nt.number-theory
2020-04-13 through 2020-04-17
International Centre for Mathematical Sciences
Edinburgh, Scotland; UK

Meeting Type: conference

Contact: Alex Bartel, Alice Silverberg

Description

The purpose of the workshop is to bring together leading, as well as early career researchers on arithmetic statistics and on algorithmic aspects of algebra and number theory, with the aim of fostering collaborations within and between these communities, and to offer early career researchers the opportunity to get a broad overview of the most recent achievements and of the most pressing problems in these fields. Another purpose is to celebrate the mathematics of Hendrik W. Lenstra Jr. on the occasion of his 71st birthday.

Lattices: From Theory to Practice

nt.number-theory
2020-04-27 through 2020-05-01
Simons Institute for the Theory of Computing
Berkeley, CA; USA

Meeting Type: conference

Contact: see conference website

Description

Recent trends, such as the NIST initiative to standardize post-quantum cryptography, point to large-scale adoption of lattice-based cryptography in the near future. There has consequently been a great deal of attention devoted to making various aspects of lattice-based cryptography practical.

This workshop will focus on questions related to the transition of lattice-based cryptography from theory to practice including the hardness of lattice problems arising from algebraic number theory, and algorithmic solutions to practical issues such as time and space-efficiency, side-channel resistance, and ease of hardware implementations.

The workshop will bring together theoretical and applied cryptographers and computational number-theorists, and will also encourage interaction amongst different communities within and outside cryptography.

May 2020

The Arithmetic of the Langlands Program

ag.algebraic-geometry nt.number-theory rt.representation-theory
2020-05-04 through 2020-08-21
Hausdorff Research Institute for Mathematics
Bonn; Germany

Meeting Type: conference

Contact: see conference website

Description

none

Summer School: The Arithmetic of the Langlands Program

ag.algebraic-geometry nt.number-theory rt.representation-theory
2020-05-11 through 2020-05-15
Hausdorff Research Institute for mathematics
Bonn; Germany

Meeting Type: summer school

Contact: see conference website

Description

none

Foundations and Perspectives of Anabelian Geometry

ac.commutative-algebra ag.algebraic-geometry nt.number-theory
2020-05-18 through 2020-05-22
RIMS
Kyoto; Japan

Meeting Type: conference

Contact: see conference website

Description

This workshop is one of the workshops of a special RIMS year "Expanding Horizons of Inter-universal Teichmüller Theory". The workshop will review fundamental developments in several branches of anabelian geometry, as well as report on recent developments. The list of speakers includes major contributors to anabelian geometry and birational anabelian geometry. Anabelian geometry, together with higher class field theory and the Langlands correspondences, is one of three generalisations of class field theory.

June 2020

Arithmetic Geometry, Number Theory, and Computation III

ag.algebraic-geometry nt.number-theory
2020-06-01 through 2020-06-05
ICERM
Providence, RI; USA

Meeting Type: conference

Contact: Andrew V. Sutherland

Description

none

Advances in Mixed Characteristic Commutative Algebra and Geometric Connections

ac.commutative-algebra ag.algebraic-geometry nt.number-theory
2020-06-07 through 2020-06-12
Casa Matemática Oaxaca (CMO)
Oaxaca; Mexico

Meeting Type: conference

Contact: see conference website

Description

The Casa Matemática Oaxaca (CMO) will host the "Advances in Mixed Characteristic Commutative Algebra and Geometric Connections" workshop in Oaxaca, from June 7 to June 12, 2020.

One of the big ideas in modern mathematics is that integers (like 1, 2, 3, 4, 5, ...) in many formal ways behave similarly to polynomial equations (like y = x^2, which defines the parabola). Frequently, and perhaps surprisingly, many questions in mathematics are easier to study for polynomials than for integers. Hence intuition and results for polynomials can tell us about the integers. Commutative algebra lives at the intersection of both perspectives, and one fundamental object of study is polynomials with integer coefficients, this is called the mixed characteristic case. Recently, Yves Andre proved a long standing open conjecture in commutative algebra in this mixed characteristic setting, relying on constructions of Scholze (and then Bhatt gave a simplified proof of the same conjecture).

This workshop aims to foster and discuss these and other recent tools, to study some remaining open problems in mixed characteristic. The workshop will bring together a diverse group of researchers from different fields, such as commutative algebra, algebraic geometry, and number theory.

Connecticut Summer School in Number Theory

nt.number-theory
2020-06-08 through 2020-06-14
University of Connecticut
Storrs, CT; USA

Meeting Type: summer school and conference

Contact: Jennifer Balakrishnan, Keith Conrad, Alvaro Lozano-Robledo, Christelle Vincent, Liang Xiao

Description

CTNT 2020 will take place during the week of June 8th-14th, 2020 (summer school June 8-12, and research conference 12-14), at University of Connecticut.

Foundations of Computational Mathematics (FoCM) 2020

ag.algebraic-geometry nt.number-theory
2020-06-15 through 2020-06-24
Simon Fraser University
Vancouver, BC; Canada

Meeting Type: conference

Contact: see conference website

Description

none

Canadian Number Theory Association (CNTA XVI)

nt.number-theory
2020-06-22 through 2020-06-26
Toronto, Ontario; Canada

Meeting Type: conference

Contact: Patrick Ingram

Description

none

Combinatorial Anabelian Geometry and Related Topics

ag.algebraic-geometry
2020-06-29 through 2020-07-03
RIMS, Kyoto University
Kyoto; Japan

Meeting Type: conference

Contact: see conference website

Description

Combinatorial anabelian geometry concerns the reconstruction of scheme- or ring-theoretic objects from more primitive combinatorial constituent data. In this sense, it is closely philosophically related to inter-universal Teichmüller theory.

The purpose of the present workshop is to expose fundamental, introductory aspects of combinatorial anabelian geometry, as well as more recent developments related to the Grothendieck-Teichmüller group and the absolute Galois groups of number fields and mixed-characteristic local fields.

The workshop will also treat results concerning the "resolution of nonsingularities" of hyperbolic curves over mixed-characteristic local fields, such results are closely related to combinatorial anabelian geometry over mixed-characteristic local fields.

July 2020

Park City Mathematics Institute: Number theory informed by computation

nt.number-theory
2020-07-05 through 2020-07-25
IAS/PCMI
Park City, UT; USA

Meeting Type: conference and summer school

Contact: Bjorn Poonen

Description

none

Workshop on Local Langlands and p-adic methods

ag.algebraic-geometry nt.number-theory rt.representation-theory
2020-07-13 through 2020-07-17
Hausdorff Research Institute for Mathematics
Bonn; Germany

Meeting Type: conference

Contact: see conference website

Description

none

Arithmetic Geometry

ag.algebraic-geometry nt.number-theory
2020-07-19 through 2020-07-25
MFO
Oberwolfach; Germany

Meeting Type: conference

Contact: see conference website

Description

none

August 2020

Stacks Project Workshop 2020

ag.algebraic-geometry nt.number-theory
2020-08-03 through 2020-08-07
University of Michigan
Ann Arbor, MI; USA

Meeting Type: workshop (appropriate for graduate students)

Contact: Pieter Belmans, Aise Johan de Jong, Wei Ho

Description

This will be a workshop in arithmetic and algebraic geometry, similar to the previous iteration (https://stacks.github.io/2017/). The intended participant is a graduate student, or a postdoc, or even a senior researcher. You will work on a single topic in a small group together with a mentor for a week with the aim of producing a text that will be considered for inclusion in the Stacks Project. Part of this process will be seeing how one builds new theory from the foundations. There will also be one or two talks per day covering advanced topics in arithmetic or algebraic geometry.

The Stacks project workshop will have some optional activities you won't see at other workshops. Adding references to and finding mistakes in the Stacks Project (and fixing them) as well as activities related to LaTeX use, Git, and GitHub. Overall these will be aimed at helping you contribute efficiently to the Stacks Project.

Workshop on Global Langlands, Shimura varieties, and shtukas

ag.algebraic-geometry nt.number-theory rt.representation-theory
2020-08-17 through 2020-08-21
Hausdorff Research Institute for Mathematics
Bonn; Germany

Meeting Type: conference

Contact: see conference website

Description

none

Decidability, definability and computability in number theory

ag.algebraic-geometry lo.logic nt.number-theory
2020-08-17 through 2020-12-18
MSRI
Berkeley, CA; USA

Meeting Type: research program

Contact: see conference website

Description

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

Connections for Women: Decidability, definability and computability in number theory

ag.algebraic-geometry lo.logic nt.number-theory
2020-08-20 through 2020-08-21
MSRI
Berkeley, CA; USA

Meeting Type: conference

Contact: see conference website

Description

The aim of the workshop is to discover how the problems in number theory and algebraic geometry arising from the Hilbert’s tenth problem for rationals interact with the ideas and techniques in mathematical logic, such as definability from model theory and decidability and degree-theoretic complexity from computability theory. This interaction includes various analogues of Hilbert’s tenth problem and related questions, focusing on the connections of algebraic, number-theoretic, model-theoretic, and computability-theoretic properties of structures and objects in algebraic number theory, anabelian geometry, field arithmetic, and differential algebra.

Low-Dimensional Topology and Number Theory

gt.geometric-topology nt.number-theory
2020-08-23 through 2020-08-29
MFO
Oberwolfach; Germany

Meeting Type: conference

Contact: see conference website

Description

none

Introductory Workshop: Decidability, definability and computability in number theory

nt.number-theory lo.logic
2020-08-24 through 2020-08-28
MSRI
Berkeley, CA; USA

Meeting Type: conference

Contact: see conference website

Description

Our workshop will focus research efforts on the interaction of number-theoretic questions with questions of decidability, definability, and computability, bringing together researchers approaching these questions from various sides to work on the core issues. This Introductory Workshop will serve as the introductory event of the MSRI semester program and is designed to introduce the basic structures and ideas of the different communities, and to highlight problems of active current interest.

Modern Breakthroughs in Diophantine Problems

nt.number-theory
2020-08-30 through 2020-09-04
Banff International Research Station
Banff; Canada

Meeting Type: conference

Contact: see conference website

Description

none

Automorphic Forms and Arithmetic

ag.algebraic-geometry nt.number-theory rt.representation-theory
2020-08-30 through 2020-09-05
MFO
Oberwolfach; Germany

Meeting Type: conference

Contact: see conference website

Description

none

September 2020

Arithmetic Aspects of Algebraic Groups

ag.algebraic-geometry gr.group-theory nt.number-theory
2020-09-06 through 2020-09-11
BIRS
Banff, AB; Canada

Meeting Type: conference

Contact: see conference website

Description

The Banff International Research Station will host the "Arithmetic Aspects of Algebraic Groups" workshop in Banff from September 6 to September 11, 2020.

The investigation of arithmetic groups has been an active and important area of mathematical research ever since it arose in the work of Gauss, Klein, Poincare, and other famous mathematicians of the 18th and 19th centuries. New points of view have recently led to progress on classical problems, opened new directions of inquiry, and revealed unexpected connections with other areas of mathematics. The workshop will bring together experts in the area, researchers in related fields, and young mathematicians who wish to learn about the most recent advances and the most promising directions for the future of the field.

Géométrie algébrique, Théorie des nombres et Applications

ag.algebraic-geometry nt.number-theory
2020-09-21 through 2020-09-25
University of French Polynesia
Papeete; French Polynesia

Meeting Type: conference

Contact: see conference website

Description

The GTA 2020 conference brings together world class researchers in mathematics. Its main objectives are to discuss recent advances in the fields of algebraic geometry, number theory and their applications, as well as to foster international collaborations on related topics.

November 2020

WIN5: Women in Numbers 5

ag.algebraic-geometry nt.number-theory
2020-11-15 through 2020-11-20
BIRS
Banff, AB; Canada

Meeting Type: conference

Contact: see conference website

Description

The Banff International Research Station will host the "WIN5: Women in Numbers 5" workshop in Banff from November 15 to November 20, 2020.

Despite recent progress in gender equality in STEM fields, women continue to be underrepresented in the research landscape of many areas of mathematics, including number theory. The Women in Numbers (WIN) network was created in 2008 for the purpose of increasing the number of active female researchers in number theory. For this purpose, WIN sponsors regular conferences, taking place approximately every three years, where female scholars gather to collaborate on cutting-edge research in the field and produce publishable scientific results. The WIN workshops provide an ongoing forum for involving each new generation of junior faculty and graduate students in state-of-the-art research in number theory. They have to come be highly regarded among the broader number theory community due to the quality of research produced by these collaborations.

WIN5 is the fifth in this series of events, bringing together female number theorists at various career stages for research collaboration and mentorship. As always, the scientific program will centre on onsite collaboration on open research problems in number theory, conducted in small groups comprised of senior and junior scholars as well as graduate students. Groups will publish their initial finding in a peer-reviewed conference proceedings volume, and research partnerships formed at the WIN5 workshop are expected to last well beyond the duration of the event. WIN projects have the potential to grow into fruitful long-term research alliances that have a transforming influence on participants' careers and a significant positive impact on the research landscape in number theory. Past WIN workshop project groups have matured into highly effective research teams producing ongoing scholarly work of exceptional scientific quality.

Langlands Program: Number Theory and Representation Theory

ag.algebraic-geometry nt.number-theory rt.representation-theory
2020-11-29 through 2020-12-04
Casa Matemática Oaxaca (CMO)
Oaxaca; Mexico

Meeting Type: conference

Contact: see conference website

Description

The Casa Matemática Oaxaca (CMO) will host the "Langlands Program: Number Theory and Representation Theory" workshop in Oaxaca, from November 29 to December 04, 2020.

Langlands functoriality conjectures predict a vast generalization of the classical reciprocity laws of Class Field Theory, providing crossroads between Number Theory and Representation Theory. The conjectures are both local and global and pertain a connected reductive group and its Langlands dual group.

We aim to introduce young mathematicians in M\'exico and Latin-America to topics of current research in the Langlands Program. We will also promote the participation women and of graduate students from a diverse background in a workshop where experts in the field from across the world will gather to expand upon the frontiers of current research. In addition to research talks, there will be three courses that will also be accessible to mathematicians working in closely related fields.