## Andrei Zelevinsky : Cluster algebras via quivers with potentials

- Gergen Lectures ( 283 Views )This lecture ties together the strands developed in the first two lectures. We discuss a recent proof (due to H. Derksen, J. Weyman, and the speaker) of a series of conjectures on cluster algebras by means of the machinery of quivers with potentials. An important ingredient of our argument is a categorification of cluster algebras using quiver Grassmannians, a family of projective algebraic varieties that are a far-reaching generalization of ordinary Grassmannians. Generalizing an idea due to P. Caldero, F. Chapoton and B. Keller, we show that the Euler characteristics of these varieties carry crucial information about the structure of cluster algebras.

## Alice Guionnet : The spectrum of non-normal matrices, II: the Brown measure.

- Gergen Lectures ( 268 Views )In this talk, which is a continuation of Wednesday's lecture, we shall describe the natural candidate for the limit of the empirical measure of the eigenvalues of non-normal matrices, the so-called Brown measure. We will give some details about how to prove convergence towards such a limit, but also discuss the instability of such convergence.