Student GFA Seminar Schedule 2005-2006
| January 24th | Elias Kappos |
Overview of $L^2$-cohomology $L^2$-cohomology is the link between functional analysis and $l^p$-cohomology. The tools are coming from FA and the ideas are going to be generalized for the case $p\neq 2$. In this talk $L^2$-Betti numbers will be defined and some applications and open problems will be stated. |
| January 31st | Elias Kappos |
Introduction to the cohomology of groups Cohomology of groups provides us with the necessary techniques to generalize the ideas of $L^2$-cohomolgy to the case $p\neq 2$. The basic definitions and examples for the next talk will be discussed. |
| February 14th | Elias Kappos |
$L^p$-cohomology In the last talk of this "mini-series" I finally want to introduce the notion of $l^p$-cohomology for groups of type $FP_n$ and discuss known results. |
| February 28th | Uuye Otgonbayar |
Spectral theorem in finite dimensions I will talk about the spectral theorem we all love and adore. I will consider a very special case: unitary matrices of finite dimension. So now this is pure linear algebra: any unitary matrix is diagonalizable. I'm sure everyone has his favourite proof of this simple fact, but I will present two slightly nonconventional proofs, one differential topological and one algebraic topological. |
| March 21st | Bram Mesland |
The Gohberg/Krein index theorem I will talk about the Gohberg/Krein index theorem, which can be proved using cyclic homology. Although it can be proved by less sophisticated methods, I think it illustrates well the compatibility of K/theory and cyclic homology and the use of Chern characters without getting too complicated. |
| April 4th | Uuye Otgonbayar |
Kaplansky conjecture for free group on finitely many generators We've been learning about K-theory and cyclic theory at the GFA seminar. Today I will talk about an application of these abstract ideas to a very concrete problem, namely: is there a non-trivial idempotent in the group algebra of a free group on finite generators? The main ingredient of the solution I present (due to Connes and others) is a specific Fredholm module whose 0-th Chern character is the trace. The construction of this Fredholm module rests on ideas in Haagerup's paper Nigel talked about today. |
