Séminaires : Séminaire des Thésards

Le séminaire des thésards est l'occasion pour les doctorants de présenter des résultats et des problématiques dignes d'intérêt devant un public de non-spécialistes. L'ambiance y est informelle ; poser des questions naïves est encouragé, et les questions moins naïves sont bienvenues dans la mesure où elles n'entravent pas le bon déroulement de l'exposé.

Un jeudi sur deux à 18h00, en alternance entre Jussieu et Sophie Germain.

Cluster algebras were introduced in the late 90's by Fomin and Zelevinsky out of attempts to understant the combinatorics of canonical bases for quantum groups. Cluster algebras turned out to be very interesting in themselves and many connections appeared with various fields of mathematics, such as tropical geometry, representation theory, knot theory, Poisson geometry, etc.

In 2008, Hernandez and Leclerc proposed to identify cluster algebras with Grothendieck rings of categories appearing in representation theory. The idea is that there should be a correspondence between generators of a cluster algebra A and certain distinguised objects in a category C. In this framework we will explain how such correspondence can yield relationships between parametrizations of simple objects in C and cluster algebra invariants. Using the recent works of Kand-Kashiwara-Kim-Oh, we will focus on the case of categorification of cluster algebras via representations of quiver Hecke algebras.