Masaki Kashiwara (Kyoto University)

Conférences dans le cadre de l'atelier sur la théorie combinatoire de représentation (21-25 avril 2014)
Lectures at the Workshop on Combinatorial Representation Theory (April 21-25, 2014)

Lundi 21 avril 2014, 16h00
Mosday, April 21, 2014, 4:00 pm

Symmetric quiver Hecke algebras and R-matrix

Résumé/Abstract : By using the R-matrices between finite-dimensional modules over a quantum affine algebra, we can construct a functor from the category of finite-dimensional representations of quiver Hecke algebras (Khovanov-Lauda-Rouquier algebras) to the category of finite-dimensional modules over quantum affine algebras. It is a joint work with Seok-Jin Kang and Myugho Kim.

Mardi 22 avril 2014, 16h00
Tuesday, April 22, 2014, 4:00 pm

Parameters of quiver Hecke algebras

Résumé/Abstract : The Grothendieck group of the category of finite-dimensional modules over a quiver Hecke algebra is isomorphic to the half of the quantum group. Varagnolo-Vasserot and Rouquier proved that, the simple modules over the quiver Hecke algebra correspond to the upper global basis, when it is associated with a symmetric generalized Cartan matrix. Indeed, a quiver Hecke algebra depends on parameters and what they proved is at a special choice of parameters. In this talk, we explain the simple modules over the quiver Hecke algebras with generic parameters also correspond to the upper global basis in a symmetric generalized Cartan matrix case.

LIEU/VENUE :
Centre de recherches mathématiques
Pavillon André-Aisenstadt, Université de Montréal
Salle / Room 6214

Diaporama de la conférence / Lecture slideshow

Conférence s'adressant à un large auditoire
Lecture suitable for a general audience

Jeudi 24 avril 2014, 16h00
Thursday, April 24, 2014, 4:00 pm

Riemann-Hilbert correspondence for irregular holonomic
D-modules

Résumé/Abstract : The original Riemann-Hilbert problem is to construct a linear ordinary differential equation with regular singularities whose solutions have a given monodromy. Nowadays, it is formulated as a categorical equivalence between the category of regular holonomic D-modules and the category of perverse sheaves. However it is a long standing problem to describe linear ordinary differential equations with irregular singularities in a geometric language.

Recently, I, with Andrea D'Agnolo, proved a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular (arXiv:1311.2374). In this correspondence, we have to replace the derived category of constructible sheaves with a full subcategory of ind-sheaves (or subanalytic sheaves) on the product of the base space and the real projective line.

LIEU/VENUE :
Centre de recherches mathématiques
Pavillon André-Aisenstadt, Université de Montréal
Salle / Room 1140

Une réception suivra la conférence au Salon Maurice-L'Abbé, Pavillon André-Aisenstadt (Salle 6245).
A reception will follow at the Salon Maurice-L'Abbé, Pavillon André-Aisenstadt (Room 6245).