Seminar

Classification of the irreducible representations of braid groups

Abstract: In this talk I'm going to discuss the classification of the
irreducible representations of the Artin braid group $B_n$ on $n$ strings. All
irreducible representations of $B_n$ of dimension  less or equal to $n-1$
were classified by Ed Formanek in 1996; the irreducible representations of
$B_n$ of dimension  $n$ for $n\geq 9$ were classified by the speaker in 1999,
and for $n \leq 8$ they were classified by Formanek, Lee, Vazirani and the
speaker in 2003.

The Margulis Superrigidity Theorem

A lattice is a special kind of discrete subgroup of a topological group. The Margulis superrigidity theorem says, roughly, that if the group satisfies certain conditions then the structure of the lat-tice has a surprising amount of influence on the structure of the group. For this and related work, Grigory Margulis won the Fields Medal in 1978. I’ll try to present some of these ideas in a way un-derstandable to grad students of all backgrounds

Equivariant cohomology, momentum graphs and Chinese remainder theorem

Abstract: I will start with defining the notion of equivariant cohomology for a group action on a topological space. It is a ring that encodes information both about the topology of the space as well as the action of the group. Often equivariant cohomology is easier to compute and one can recover the usual cohomology of a space from its equivariant cohomology.

A new mixed-FEM for steady-state natural convection models allowing conservation of momentum and thermal energy

In this work we present a new mixed finite element method for a class of natural convection models describing the behavior of non-isothermal incompressible fluids subject to a heat source. More precisely, we consider a system based on the coupling of the steady-state equations of momentum (Navier-Stokes) and thermal energy by means of the Boussinesq approximation.

A Banach space mixed formulation for the unsteady Brinkman-Forchheimer equations

We propose and analyze a mixed formulation for the Brinkman-Forchheimer equations for unsteady flows. Our approach is based on the introduction of a pseudostress tensor related to the velocity gradient, leading to a mixed formulation where the pseudostress tensor and the velocity are the main unknowns of the system. We establish existence and uniqueness of a solution to the weak formulation in a Banach space setting, employing classical results on nonlinear monotone operators and a regularization technique.