Past Kinderseminar

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.

21 October 2015
11:00
to
12:30
Gareth Wilkes
Abstract

I will give a historical overview of some of the theorems proved by the
Ancient Greeks, which are now taken for granted but were, and are,
landmarks in the history of mathematics. Particular attention will be
given to the calculation of areas, including theorems of Hippocrates,
Euclid and Archimedes.

14 October 2015
11:00
to
12:30
Rob Kropholler
Abstract

Many people talk about properties that you would expect of a group. When they say this they are considering random groups, I will define what it means to pick a random group in one of many models and will give some properties that these groups will have with overwhelming probability. I will look at the proof of some of these results although the talk will mainly avoid proving things rigorously.

16 June 2015
11:00
to
12:30
Thomas Wasserman
Abstract

This'll be a nice and slow paced introduction to topological quantum field theory in general, and 1-2-3 dimensional theories in particular. If time permits I will explain the spin version of these and their connection to physics. There will be lots of pictures. 

10 June 2015
11:00
to
12:30
Chris Nicholls
Abstract

In the classification of surfaces, K3 surfaces hold a place not dissimilar to that of elliptic curves within the classification of curves by genus. In recent years there has been a lot of activity on the problem of rational points on K3 surfaces. I will discuss the problem of finding the Picard group of a K3 surface, and how this relates to finding counterexamples to the Hasse principle on K3 surfaces.

27 May 2015
11:00
to
12:30
Henry Bradford
Abstract

Expansion, rank gradient and virtual splitting are all concepts of great interest in asymptotic group theory. We discuss a result of Marc Lackenby which demonstrates a surprising relationship between then, and give examples exhibiting different combinations of asymptotic behaviour.

6 May 2015
11:00
to
12:30
Robert Kropholler
Abstract

With the general election looming upon I will discuss the various different kinds of voting system that one could implement in such an election. I will show that these can give very different answers to the same set of voters. I will then discuss Arrow's Impossibility Theorem which shows that no voting system is compatible with 4 simple axioms which may be desireable.

11 March 2015
11:00
to
12:30
Henry Bradford
Abstract

Expansion, Random Walks and Sieving in $SL_2 (\mathbb{F}_p[t])$

 

We pose the question of how to characterize "generic" elements of finitely generated groups. We set the scene by discussing recent results for linear groups in characteristic zero. To conclude we describe some new work in positive characteristic.

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