Past Kinderseminar

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>
9 February 2011
11:30
Maria Buzano
Abstract
This talk will be divided into three parts. In the first part we will recall basic notions and facts of differential geometry and the Ricci flow equation. In the second part we will talk about singularities for the Ricci flow and Ricci flow on homogeneous spaces. Finally, in the third part of the talk, we will focus on the case of Ricci flow on compact homogeneous spaces with two isotropy summands.

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