Conférences  >  Mathématiques  >  Théorie des groupes

Lie groups are central objects in modern mathematics; they arise as the automorphism groups of many homogeneous spaces, such as flag manifolds and Riemannian symmetric spaces. Often, one can construct manifolds locally modelled on these homogeneous spaces by taking quotients of their subsets by discrete subgroups of their automorphism groups. Studying such discrete subgroups of Lie groups is an active and growing area of mathematical research. The objective of this summer school is to introduce young researchers to a class of discrete subgroups of Lie groups, called Anosov subgroups. These subgroups are central objects in the study of higher Teichmuller theory, convex projective geometry, and character varieties. In this summer school, there will be an emphasis on discussing some of the dynamical tools that have recently been successfully used to study Anosov subgroups. The required background in dynamics, hyperbolic geometry, and Lie theory will also be discussed. Aside from providing a stimulating academic environment for learning about Anosov subgroups, this summer school also aims to be a relaxed and friendly space for participants to interact with fellow aspiring mathematicians.

Géométrie et topologie,    Cours et évènements pour étudiants en mathématiques

The Fields Institute for Research in Mathematical Sciences

This intensive graduate school will cover topics central to the Workshop on Interactions between Group Theory and Homotopy Theory the following week. This school is designed to give graduate students and early career researchers in related fields a better understanding of each subject, thus enabling the participants to better engage in the subsequent workshop.

Géométrie et topologie,    Cours et évènements pour étudiants en mathématiques

The Fields Institute for Research in Mathematical Sciences

Group theory and topology have a long and rich history of interaction. This workshop will bring together experts working on different aspects of this interaction in order to share ideas and boost the development of new methods that can be applied to the topology of configuration spaces, braid groups, mapping class groups and manifolds, and spaces of commuting elements.

Géométrie et topologie,    Cours et évènements pour étudiants en mathématiques

American Institute of Mathematics, Pasadena, California (AIM)

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

This program will focus on several aspects of the theory of automorphic forms with an emphasis on the relations among the internal structure of spaces of automorphic forms, the Langlands functoriality principle, automorphic L-functions, and questions in geometry, in particular, those regarding locally symmetric spaces. These are associated with arithmetic subgroups of a given reductive algebraic group G dened over analgebraic number field. Special attention is given to the theory of Eisenstein series and their ubiquitous role within the theory of automorphic forms.

Géométrie et topologie,    Cours et évènements pour étudiants en mathématiques

University of Münster

Statistique, Théorie des jeux,    Cours et évènements pour étudiants en mathématiques

Banach Center

Since its origins in the work of Sophus Lie (now more than a century ago), Lie theory has seen tremendous developments and is now fundamental in many areas of mathematics (like group theory, geometry, symmetric spaces etc) and physics (quantum mechanics, particle physics, theory of gravity). Nowadays there are specialized computer packages such as LiE, the Atlas project, the package Chevie for GAP3, the program ChevLie. Also the more general purpose computer algebra systems GAP4, MAGMA and SageMath have large libraries for dealing with various objects that are central to Lie theory.

The conference aims at bringing the eminent Number Theorists worldwide in the domain of Algebraic Number Theory and young scholars from the country on a common platform to project their work, and foster collaborations to further the development of Mathematical Research.

The areas of particular interest include: Ideal class groups of number fields (algebraic, analytic and computational aspects), Relative class numbers of number fields, Annihilators of class groups, Class field theory, Picard groups, Selmer groups, Diophantine equations, Elliptic curves, Iwasawa Theory, Modular forms and related topics.

Algèbre,    Théorie des nombres, arithmétique

Institute for Computational and Experimental Research in Mathematics, Brown University, Providence, RI (ICERM)

The diagrammatic approach has its origins in the discovery of new quantum invariants of knots and links in the 1980s. Crane and Frenkel raised the idea of categorifying quantum groups, hence, link invariants, already in the 1990s, and this vision prompted the development of powerful link homology theories such as Khovanov-Rozansky homology. The categorification of quantum groups involves Khovanov-Lauda-Rouquier algebras, which are often presented diagrammatically. They are a building block for Kac-Moody 2-categories, which categorify Lusztig’s modified integral form for quantized enveloping algebra. There have been many remarkable developments in this direction in the last few years, including the introduction by Webster of more general algebras categorifying tensor products, DG versions of these algebras which categorify Verma modules, and p-DG versions which are being used to categorify link invariants at roots of unity. The field of diagrammatic categorification is still in its early stages, but it has already had a significant impact on more traditional mathematics. This workshop aims to unite both established experts and emerging scholars across various domains of diagrammatic categorification, including representation theory, combinatorics, and link homology.

Institute for Computational and Experimental Research in Mathematics, Brown University, Providence, RI (ICERM)

Webs are diagrammatic tools for representing complex calculations graphically. These diagrams first arose from the representation theory of classical groups, and they have since become important in disparate areas of mathematics. In representation theory, they encode morphisms of quantum groups. In topology, webs give rise to powerful link invariants. In algebra and geometry, Kuperberg's \(mathrm{sl}(3)\) web bases have important relationships with the theory of cluster algebras and affine buildings. In combinatorics, they explain certain dynamics on Young tableaux. Recent work by Gaetz--Pechenik--Pfannerer--Striker--Swanson introduced an \(\mathrm{sl}(4)\) web basis that has exploited and extended exciting connections between webs, plabic graphs, and crystals. There are further connections to total positivity, duality conjectures for cluster algebras and mirror symmetry.

Théorie des graphes et combinatoire,    Algèbre