Seminars Sorted by Series

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...

The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of the local Langlands program is...

In joint work with Andy Manion, we required a generalization of the tensor product of 2-representations in order to reconstruct the 2-dimensional part of Lipshitz-Oszvath-Szabo’s bordered Heegaard-Floer theory. I will discuss this and possible...

Given a maximal torus $T$ of a connected reductive group $G$ over a local field $F$, there does not exist a canonical embedding of the L-group of $T$ into the L-group of $G$. Generalizing work of Adams and Vogan in the case $F=R$, we will construct...

In an ongoing project of D. Ben-Zvi, Y. Sakellaridis and A. Venkatesh, the authors propose a conjectural generalization of the derived Satake equivalence for complex reductive groups to spherical varieties. I will describe a program aimed at...

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...

Let $g$ be a semisimple Lie algebra. The affine W-algebra associated to $g$ is a topological algebra which quantizes the algebraic loop space of the Kostant slice. It is constructed as a quantum Hamiltonian (alias quantum Drinfeld--Sokolov)...

Let $I= (f_t)_{t \in [0,1]}$ be an identity isotopy on an oriented surface $M$ and denote by $Cont(I)$ the set of points $z \in M$ whose trajectory $I(z)$ is a contractible loop of $M$. A recent result of Olivier Jaulent asserts that there exists an...

This is a joint work with Renato Iturriaga.

We consider a Hamiltonian $H: \mathbf R^n \times \mathbf R \to \mathbf R, \ (x,p) \mapsto H(x,p)$ that is $Z^n$ periodic in the first variable $x$, and convex superlinear in the second variable $p$.

For $...

Let $\phi : \mathbb R\times X\to X$ be a dynamical system, an $\mathbb R$-action, defined on the metric space $X$. A nonempty, closed invariant set is minimal if it contains no proper, nonempty, closed invariant subset. We will show a construction...

I will describe an example of a $C^\infty$ volume preserving topologically transitive diffeomorphism of a compact smooth Riemannian manifold which is ergodic (indeed is Bernoulli) on an open and dense subset $U$ of not full measure and has zero...

We prove that there is an open and dense set in the C2 topology of riemannian metrics on the 2-sphere whose geodesic flow has an elliptic closed geodesic.

This result recovers, in a generic sense, a theorem by H. Poincaré 1904 and proves a conjecture...