Past Kinderseminar

1 May 2013
11:30
Elizaveta Frenkel
Abstract
<p>I shall talk about Subgroup Membership Problem for amalgamated products of finite rank free groups. I'm going to show how one can solve different versions of this problem in amalgams of free groups and give an estimate of the complexity of some algorithms involved. &nbsp;This talk is based on a joint paper with A. J. Duncan. </p>
6 March 2013
10:30
Emily Cliff -- Queen's Lecture C
Abstract
<p>We'll provide some motivation for the appearance of factorization algebras in physics, before discussing the definition of a factorization monoid. We'll then review the definition of a principal G-bundle and show how a factorization monoid can help us understand the moduli stack Bun_G of principal G-bundles.</p>
20 February 2013
10:30
Nicholas Cooney -- Queen's Lecture C
Abstract
I will give an introduction to The McKay Correspondence, relating the irreducible representations of a finite subgroup Γ ≤ SL2 (C), minimal resolutions of the orbit space C2 /Γ, and affine Dynkin diagrams.
13 February 2013
10:30
Ben Green (Oxford) -- Queen's Lecture C
Abstract
<p>A number is called transcendental if it is not algebraic, that is it does not satisfy a polynomial equation with rational coefficients. It is easy to see that the algebraic numbers are countable, hence the transcendental numbers are uncountable. Despite this fact, it turns out to be very difficult to determine whether a given number is transcendental. In this talk I will discuss some famous examples and the theorems which allow one to construct many different transcendental numbers. I will also give an outline of some of the many open problems in the field.</p>
6 February 2013
10:30
Elisabeth Fink -- Queen's Lecture C
Abstract
<p>In the Greek mythology the hydra is a many-headed poisonous beast. When cutting one of its heads off, it will grow two more. Inspired by how Hercules defeated the hydra, Dison and Riley constructed a family of groups defined by two generators and one relator, which is an Engel&nbsp; word: the hydra groups. I will talk about its remarkably wild subgroup distortion and its hyperbolic cousin. Very recent discussions of Baumslag and Mikhailov show that those groups are residually torsion-free nilpotent and they introduce generalised hydra groups.</p>
30 January 2013
10:30
Henry Bradford -- Queen's Lecture C
Abstract
<p>I will look at some tools for proving expansion in the Cayley graphs of finite quotients of a given infinite group, with particular emphasis on Bourgain-Gamburd’s work on expansion in Zariski-dense subgroups of SL_2(Z), and speculate to what extent such expansion may be said to be “uniform”.</p>
23 January 2013
10:30
Martin Palmer -- Queen's Lecture C
Abstract

There appears to be no universally accepted rigorous definition of a "flexagon" (although I will try to give a reasonable one in the talk). Examples of flexagons were most likely discovered and rediscovered many times in the past - but they were "officially" discovered in 1939, a serendipitous consequence of the discrepancy between US paper sizes and sensible paper sizes.* I'll describe a couple of the most famous examples of flexagons (with actual models to play with of course), and also introduce some of the more abstract theory of flexagons which has been developed. Feel free to bring your own models of flexagons!

* The views expressed herein are solely those of the speaker, and do not reflect the official position of the Kinderseminar w.r.t. international paper standards. 

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