# Past Kinderseminar

4 December 2013
10:30
Giles Gardam
Abstract
Kazhdan introduced property (T) for locally compact topological groups to show that certain lattices in semisimple Lie groups are finitely generated. This talk will give an introduction to property (T) along with some first consequences and examples. We will finish with a classic application of property (T) due to Margulis: the first known construction of expanders.
• Kinderseminar
27 November 2013
10:30
Mark Penney
Abstract
I will discuss what it means to compactify complex Lie groups and introduce the so-called "Wonderful Compactification" of groups having trivial centre. I will then show how the wonderful compactification of PGL(n) can be described in terms of complete collineations. Finally, I will discuss how the new perspective provided by complete collineations provides a way to construct compactifications of arbitrary semisimple groups.
• Kinderseminar
20 November 2013
10:30
Montserrat Casals
Abstract
<div>In this talk I will introduce the class of limit groups and discuss its characterisations from several different perspectives: model-theoretic, algebraic and topological.&nbsp;I hope that everyone will be convinced by at least one of the approaches that this class of groups is worth studying.</div>
• Kinderseminar
13 November 2013
10:30
Levon Haykazyan
Abstract
<p>(A simplified version of) Ax-Grothendieck Theorem states that every injective polynomial map from some power of complex numbers into itself is surjective. I will present a simple model-theoretical proof of this fact. All the necessary notions from model theory will be introduced during the talk. The only prerequisite is basic field theory.</p>
• Kinderseminar
6 November 2013
10:30
Antonio de Capua
Abstract
A large class of links in $S^3$ has the property that the complement admits a complete hyperbolic metric of finite volume. But is this volume understandable from the link itself, or maybe from some nice diagram of it? Marc Lackenby in the early 2000s gave a positive answer for a class of diagrams, the alternating ones. The proof of this result involves an analysis of the JSJ decomposition of the link complement: in particular of how does it appear on the link diagram. I will tell you an outline of this proof, forgetting its most technical aspects and explaining the underlying ideas in an accessible way.
• Kinderseminar
30 October 2013
11:30
Robert Kropholler
Abstract
I will look at the classical constructions that can be made using a straight edge and compass, I will then look at the limits of these constructions. I will then show how much further we can get with Origami, explaining how it is possible to trisect an angle or double a cube. Compasses not supplied.
• Kinderseminar
23 October 2013
11:30
Tara Brough
Abstract
<div>The <i>word problem</i> of a group $G$ with respect to a generating set $X$ is the set of all words in elements of $X$ and their inverses which represent the identity in $G$. &nbsp;A <i>formal language </i>is a set of words over a finite alphabet, and so word problems of groups can be viewed as formal languages.</div> <div>In this talk I will give an introduction to formal languages, concentrating on context-free languages and several related classes. &nbsp;I will define these languages by means of automata. &nbsp;I will then give a survey of research on groups whose word problem belongs to the language classes I have introduced, beginning with the classification of groups with context-free word problem (Muller and Schupp, 1983). &nbsp;I will also discuss some of the open problems in this area.</div>
• Kinderseminar
16 October 2013
11:30
Abstract
<p>I shall outline a procedure for efficiently approximating arbitrary elements of certain topological groups by words in a finite set. The method is suprisingly general and is based upon the assumption that close to the identity, group elements may be easily expressible as commutators. Time permitting, I shall discuss some applications to uniform diameter bounds for finite groups and to quantum computation.</p>
• Kinderseminar
12 June 2013
11:30
Emanuele Ghedin
Abstract
Symplectic reflection algebras are an important class of algebras related to an incredibly high number of different topics such as combinatorics, noncommutative geometry and resolutions of singularities and have themselves a rich representation theory. We will recall their definition and classification coming from symplectic reflection groups and outline some of the results that have characterised their representation theory over the last decade, focusing on the link with representations of quivers.
• Kinderseminar
5 June 2013
11:30
Jason Semeraro
Abstract
Saturated fusion systems are both a convenient language in which to formulate p-local finite simple group theory and interesting structures in their own right. In this talk, we will start by explaining what is meant by a 'tree of fusion systems' and give conditions on such an object for there to exist a saturated completion. We then describe how this theory can be used to understand a class of fusion systems first considered by Bob Oliver, which are determined by modular representations of finite groups. If time permits, we will discuss joint work with David Craven towards a complete classification of such fusion systems. The talk is aimed at a general mathematical audience with some background in algebra.
• Kinderseminar