Past Kinderseminar

11 May 2016
11:00
to
12:30
Simon Bergant
Abstract

In 1924, James W. Alexander constructed a 2-sphere in R3 that is not ambiently homeomorphic to the standard 2-sphere, which demonstrated the failure of the Schoenflies theorem in higher dimensions. I will describe the construction of the Alexander horned sphere and the Antoine necklace and describe some of their properties.

4 May 2016
11:00
to
12:30
Kieran Calvert
Abstract

Since the symmetric group is a finite group it’s representation theory is not too complex, however in this special case we can realise these representations in a particular nice combinatorial way using young tableaux and young symmetrizers. I will introduce these ideas and use them to describe the representation theory of Sn over the complex numbers.

24 February 2016
11:00
to
12:30
Alex Margolis
Abstract

I will talk about a remarkable theorem by Paulin, which says
that if a one-ended hyperbolic group has infinite outer automorphism
group, then it splits over a two-ended subgroup. In particular, this
gives a condition which ensures a hyperbolic group doesn't have property
(T).

 

20 January 2016
11:00
to
12:30
Robert Kropholler
Abstract
I will go through a proof of Bieberbach's theorems proving that a group acting cocompactly on Euclidean n-space has a subgroup consisting of n independent translations. Time permitting I will also prove that there is a bound on the number of such groups for each dimension n. I will assume very little requiring only a small amount of group theory and linear algebra for the proofs. 
2 December 2015
11:30
Teresa Conde
Abstract


The representation dimension of an algebra was introduced in the early 70's by M. Auslander, with the goal of measuring how far an algebra is from having finite number of finitely generated indecomposable modules (up to isomorphism). This invariant is not well understood. For instance, it was not until 2002 that O. Iyama proved that every algebra has finite representation dimension. This was done by constructing special quasihereditary algebras. In this talk I will give an introduction to this topic and I shall briefly explain Iyama's construction.

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