# Video Lectures

### Stokes phenomena, Poisson-Lie groups and quantum groups

Let G be a complex reductive group, G? its dual Poisson-Lie group, and g the Lie algebra of G. G-valued Stokes phenomena were exploited by P. Boalch to linearise the Poisson structure on G?. I will explain how Ug-valued Stokes phenomena can be used...

### Approximating tilting modules

Using the arithmetics of quantum numbers we construct some “approximations” of tilting modules for reductive algebraic groups that might be useful for understanding the generational patterns of tilting characters conjectured by Lusztig and...

### A Hecke action on the principal block of a semisimple algebraic group

I will explain the construction of an action of the Hecke category on the principal block of representations of a connected reductive algebraic group over an algebraically closed field of positive characteristic, obtained in joint work with Roman...

### Rationality properties of complex characters of finite groups

What can one say about the fields of values of irreducible complex characters ?? of a given finite group GG? In particular when GG is a finite (quasi)simple group? What about the McKay situation'', i.e. when the degree of
?? is coprime to a fixed...

### New isolated symplectic singularities with trivial fundamental group

In 2000, Arnaud Beauville introduced the notion of symplectic singularities and raised the question of classifying isolated symplectic singularities with trivial local fundamental group: the latter condition is meant to avoid the numerous quotient...

### Webs in type C

In 1997, Kuperberg gave a generators-and-relations presentation of the monoidal category Fund, whose objects are tensor products of fundamental representations, for all rank 2 lie algebras. The general case has been an open problem since. It was...

### Ultrametric stability problems

Francesco Fournier Facio

We study stability problems with respect to families of groups equipped with bi-invariant ultrametrics, that is, metrics satisfying the strong triangle inequality. This property has very strong consequences, and this form of stability behaves very...

### Computational - Statistical gaps and the Group Testing problem

In a plethora of random models for constraint satisfaction and statistical inference problems, researchers from different communities have observed computational gaps between what existential or brute-force methods promise, and what known efficient...

### Springer, Procesi and Cherednik

The talk is based on a joint work with Pablo Boixeda Alvarez. We study equivariant Borel-Moore homology of certain affine Springer fibers and relate them to global sections of suitable vector bundles arising from Procesi bundles on Q-factorial...

### Flag manifolds over semifields I

The study of totally positive matrices, i.e., matrices with positive minors, dates back to 1930s. The theory was generalised by Lusztig to arbitrary split reductive groups using canonical bases, and has significant impacts on the theory of cluster...