الجبر

Abstract: Kac and Schofield studied the generic representations for quivers. In this talk, I will explain how we attempt to generalize their results to any finite dimensional basic associative algebra via space of presentations. I will state some analogues of the classical results. This is a joint work with Harm Derksen.

Abstract: Let C_n be the n-th Calogero-Moser space: the space of conjugacy classes of pairs of matrices (X,Y) in Mat_n(C) satisfying condition rk(XY-YX+Id_n)=1. Let G be the group of symplectic automorphisms of the free algebra C< x,y> . It is known that G acts transitively on C_n. Let G_n denotes the stabilizer of a point in C_n under G. In this talk, I will explain how to compute the groups G_n using the Bass-Serre theory of groups acting on graphs. Our computation are motivated by the fact that G_n are precisely the automorphism groups of (non-isomorphic) domains Morita equivalent to the first Weyl algebra. This joint work with Y. Berest and A. Eshmatov.

Abstract: I will talk about a birational action of the symmetric group on a polynomial ring, and in particular the invariants of this action. We encountered this action studying total positivity in loop groups, but the action also occurs as an R-matrix in Berenstein-Kazhdan's theory of geometric crystals, and also in the theory of discrete Painleve dynamical systems as studied by Noumi-Yamada.

This is joint work with Pavlo Pylyavskyy.

Abstract: TBA

Abstract: TBA