Conférences  >  Mathématiques  >  Théorie des groupes

The Research Institute for Mathematical Sciences (RIMS)

Théorie des graphes et combinatoire,    Algèbre

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Algèbre,    Théorie des graphes et combinatoire

The Fields Institute

The purpose of this conference is to create a discussion between experts that work on a number of such approaches to singular spaces as well as on the broader themes that lead to these structures: Hamiltonian group actions, completely integrable systems, and geometric quantization.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

One focus of modern number theory is to study symmetries of numbers that are roots of polynomial equations. Collections of such symmetries are called Galois groups, and they often encode interesting arithmetical information. The theory of Galois representations provides a way to understand these Galois groups and in particular, how they interact with other areas of mathematics. This workshop will investigate how these Galois representations can be put together into families, and search for new arithmetic applications of these families.

The Fields Institute

This workshop will further explore interactions between set theory, Ramsey theory, and the geometry and dynamics of Polish groups. An emphasis will be placed on the large scale geometry and dynamics of homeomorphism groups, mapping class groups of spaces of infinite type, and of automorphism groups of countable structures. It will also include work on automatic continuity in the context of transformation groups.

Geometric Group Theory

Géométrie et topologie,    Algèbre

Mathematical Sciences Research Institute (MSRI)

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

The Research Institute for Mathematical Sciences (RIMS)

Algèbre,    Physique mathématique

Mathematical Sciences Research Institute (MSRI)

The Introductory Workshop aims to provide a coherent overview of current research in algebraic cycles, L-values, Euler systems, and the many connections between them. This includes the study of special cycles on Shimura varieties and moduli spaces of shtukas, integral representations of L-values and the construction of p-adic L-functions, and the construction of Euler systems from special elements in Chow groups or higher Chow groups of Shimura varieties.

The workshop focuses on four main speakers, each giving a 4-hour mini-course on a topic in Geometric Group Theory. Their lectures present a panoramic overview over some important developments in their field with the goal to enable the participants to actively participate in the new directions of research emerging from these developments.

Géométrie et topologie,    Cours et évènements pour étudiants en mathématiques

Amirkabir University of Technology, Department of Mathematics and Computer Science

Group theory plays an important role in different branches of Mathematics, for example, Geometry, Number Theory, and Analysis. Also, group theory is one of the most powerful mathematical tools used in applied mathematics, cryptography, coding theory, steganography, quantum chemistry, spectroscopy, robotics, computer vision, and quantum computation. It allows the user to predict, interpret, rationalize, and often simplify complex theory and data. The development in each field of group theory is getting faster and deeper. This fact makes all researchers reach for a better understanding of the current works and developments, in all fields of group theory and its applications. The aim of this conference is to exchange research ideas amongst the group theorists. In addition, specialists in the subject of group theory can present their latest research works and encourage interested students to progress and widen their knowledge in group theory.

Tél.: [+98 21 64548567];     Email.: adminigtc15@aut.ac.ir

Representation and character theory, Groups and combinatorics, Geometric and combinatorial groups, Monoids, semigroups and hypergroups, Algorithmic problems in finite groups, Probabilistic methods in group theory, Permutation groups, Linear groups, Infinite groups.

CRM / Université de Montréal

Measured group theory looks at groups from a probabilistic perspective, by studying their actions on probability spaces up to orbit equivalence. It turns out that the orbit equivalence relations of these actions can remember information about the group, which has yielded classification and rigidity results, as well as new invariants such as cost, |^2-Betti numbers, and ergodic dimension. Initiated by Gromov and Zimmer, the subject has become a very fruitful area of research over the last 25 years. One reason for this is that to study the orbit equivalence relation of an action, one tries to measurably equip the orbits with various combinatorial and geometric structures (graphs, trees, CW-complexes) and investigate their characteristics (colorings, matchings, ends, |^2-Betti numbers), which often requires machinery from the corresponding subjects, and also contributes back to these subjects with new results. This two-way traffic has established new connections between Measured Group Theory and various different areas, including ergodic theory, descriptive set theory, probability theory, combinatorics, geometric group theory, Lie groups, and von Neumann algebras.

CIRM - Jean-Morlet Chair

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

CRM / Université de Montréal

This mini-school focuses on “huge” groups, such as the Cremona group and its subgroups, the homeomorphism group of a surface, the mapping class group of an infinite-type surface, a general Artin group. They can be studied through non-proper actions on nonpositively or negatively curved combinatorial spaces.

CIRM – Centre International de Rencontres Mathématiques

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

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

This conference will focus on the interactions between manifolds and submanifolds of dimensions 1, 2 and 3 and their relations to topological, geometric, and group theoretic questions in a celebration of the accomplishments and influences of Yair Minsky.

Géométrie et topologie,    Algèbre

CRM / Université de Montréal

Understanding the geometry of the finitely generated subgroups of a group informs our understanding of that group significantly. For example, some hyperbolic groups enjoy the property that every finitely generated subgroup is quasi-convex. Groups which are incoherent and groups which are algebraically fibered do not have this property. This conference aims to explore some of the many directions in this field, including quasi-convexity in other contexts.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Mathematics has a wide range of different disciplines, from algebra to geometry and from analysis to topology, etc. Some discoveries, however, are able to link several disciplines together and open a field of interplay. Two of such recent discoveries are self-similar group representations and projective spectrum of linear operators. The goal of this workshop is bring together scholars in spectral theory, representation theory, complex dynamics and other related fields to exchange and examine some recent discoveries on self-similarity and projective spectrum.

CIRM – Centre International de Rencontres Mathématiques

The proposed conference aims to bring together experts from different fields: group theory, ergodic theory, probability theory and descriptive set theory. The common interest is to study properties and invariants of infinite groups using various tools, like spectral theory, L2 theory, entropy, orbit equivalence, profinite methods, random walks and graph convergence. There is already considerable interaction between these fields and the proposed participants, but much more is needed. The conference will allow participants to assimilate each others language and will open new connections.

Statistique, Théorie des jeux,    Systèmes, contrôle et automatisation

Casa Matemática Oaxaca (CMO)

The mathematical notion of a group encapsulates our common idea of symmetry. Groups play an important role in mathematics, and their structure has profound impact in the solution of a variety of problems in pure and applied mathematics. Groups are often studied from different perspectives, putting an emphasis on qualitatively different features of their structure, and therefore leading to the resolution of problems that tend to be different in nature. The aim of this workshop is to bring together some of the leading figures in two of these areas, so that each can learn new problems and techniques from the other. This will help open new avenues of research which will advance the current state of the art.

ICMS - International Centre for Mathematical Sciences

Algèbre,    Géométrie et topologie

CRM / Université de Montréal

This workshop focuses on several themes related to the fundamental groups of 3-manifolds. The themes include: the theory character varieties, Thurston norm polytopes and fibrations, orderability, profinite rigidity, and variations on the Cannon conjecture. The first week of the workshop will feature mini-courses by Ian Biringer (Boston College), Michelle Chu (Minnesota), Nathan Dunfield (Illinois-Urbana), and Daniel Groves (Illinois-Chicago). The second week will be devoted to research talks.

CRM / Université de Montréal

The mini-courses and research talks will address several themes, including: nonpositively-curved cube complexes, median spaces, (coarsely) Helly spaces and groups, and various combinatorial notions of nonpositive curvature. The first week of the workshop involves mini-courses by Elia Fioravanti (MPI Bonn), Thomas Haettel (Université de Montpellier), Nima Hoda (ENS Paris), Nir Lazarovich (Technion). The second week will be devoted to research talks.

Géométrie et topologie,    Théorie des graphes et combinatoire

Interest in specialization of polynomials and Galois groups goes back at least to the work of Hilbert on the inverse Galois problem. This theory has found an abundance of applications in Algebra, Number Theory, Group Theory, and Arithmetic Geometry. In recent years, the area is blooming and we see striking results that open completely new horizons: The discovery of Hilbert irreducibility properties of algebraic groups, its connection with expanders and random walks, the interrelation with arithmetic-geometric properties of parametrizing varieties, and the exciting progress on the Cohen-Lenstra heuristics. The conference aims to bring together leading experts and young researchers interested in the area. We plan to leave an abundance of free time, dedicated to informal discussions. We believe that this will encourage the transfer of ideas, techniques, and will foster new collaborations and new research directions.

Algèbre,    Théorie des nombres, arithmétique

Casa Matemática Oaxaca (CMO)

In the recent development of Mathematics, the study of symmetry of highly singular objects has contributed to the simultaneous understanding of symmetries and groups. The aims of the Workshop are the study of symmetries of the Cantor set, and the understanding of the groups arising as symmetries of the Cantor set.

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

In this workshop, we want to bring together researchers from both sides of this development: those mathematicians specializing in the application of modern algebraic and algebro-geometric methods to the study of algebraic groups and their torsors, as well as those working on relevant aspects of the motivic and cohomological approaches from a more abstract viewpoint. We hope that bringing this mix of researchers together will have a synergistic impact, leading to concrete new applications of the abstract machinery to outstanding problems on quadratic forms, algebras with involution and algebraic groups, but also inspiring progress on the general development of the motivic and cohomological methods.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

The symmetries of classical mathematical objects form a group. In the past several decades, we have seen new quantum mathematical objects like von Neumann algebras and quantum field theories whose symmetries are best described by tensor categories. One reason for this is that these mathematical objects naturally form higher categories, and thus their endomorphisms naturally form higher monoidal categories. In this sense, we view fusion categories as objects which encode quantum symmetries. Subfactors are a rich source of examples of exotic unitary fusion categories, and conversely, every unitary fusion category arises from a subfactor. This correspondence leads to deep mathematical connections between these fields. These mathematical objects are also intimately related to conformal field theory and topological phases of matter, which give topological quantum field theories, in which higher categories play an important role. The purpose of this workshop is built on the 2014 and 2018 BIRS workshops on subfactors and fusion categories, with the goal of studying these objects through a higher categorical lens. To do so, we will bring together world experts from subfactors, fusion categories, higher categories, and mathematical physics to further develop the deep and rich connections between these fields.