Past Kinderseminar

1 June 2011
11:30
Elisabeth Fink
Abstract
The talk will start with the definition of amenable groups. I will discuss various properties and interesting facts about them. Those will be underlined with representative examples. Based on this I will give the definition and some basic properties of sofic groups, which only emerged quite recently. Those groups are particularly interesting as it is not know whether every group is sofic.
9 March 2011
11:30
Chloé Perin
Abstract
<p>The long-open Tarski problem asked whether first-order logic can distinguish between free groups of different ranks. This was finally answered in the negative by the works of Sela and Kharlampovich-Myasnikov, which sparked renewed interest in the model theoretic properties of free groups. I will give a survey of known results and open questions on this topic.</p>
23 February 2011
11:30
David Craven
Abstract
<p>The representation theory of the symmetric groups is far more advanced than that of arbitrary finite groups. The blocks of symmetric groups with defect group of order p<sup>n</sup> are classified, in the sense that there is a finite list of possible Morita equivalence types of blocks, and it is relatively straightforward to write down a representative from each class.</p><p>In this talk we will look at the case where n=2. Here the theory is fairly well understood. After introducing combinatorial wizardry such as cores, the abacus, and Scopes moves, we will see a new result, namely that the simple modules for any p-block of weight 2 "come from" (technically, have isomorphic sources to) simple modules for S<sub>2p</sub> or the wreath product of S<sub>p</sub> and C<sub>2</sub>.</p>

Pages