# Algebra Kinderseminar (past)

 Wed, 15/05 11:30 Jo French Algebra Kinderseminar Queen's College In this talk, I will discuss homotopy limits: The basics, and why you should care about them if you are a topologist, an algebraic geometer, or an algebraist (have I missed anyone?).
 Wed, 08/05 11:30 Thomas Wasserman Algebra Kinderseminar Queen's College Categorification is a fancy word for a process that is pretty ubiquitous in mathematics, though it is usually not referred to as "a thing". With the advent of higher category theory it has, however, become "a thing". I will explain what people mean by this "thing" (sneak preview: it involves replacing sets by categories) and hopefully convince you it is not quite as alien as it may seem and maybe even tempt you to let it infect some of your maths. I'll then explain how this fits into the context of higher categories.
 Wed, 01/05 11:30 Elizaveta Frenkel (Moscow) Algebra Kinderseminar Queen's College 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.  This talk is based on a joint paper with A. J. Duncan.
 Wed, 24/04 11:30 David Hume ((Oxford University))) Algebra Kinderseminar Queen's College Following the recent paper of Ogasa, we attempt to construct Boy's surface using only paper and tape. If this is successful we hope to address such questions as: Is that really Boy's surface? Why should we care? Do we have any more biscuits?
 Wed, 06/03 10:30 Emily Cliff -- Queen's Lecture C Algebra Kinderseminar Queen's College 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.
 Wed, 27/02 10:30 Alessandro Sisto -- Queen's Lecture C ((Oxford University))) Algebra Kinderseminar Queen's College
 Wed, 20/02 10:30 Nicholas Cooney -- Queen's Lecture C Algebra Kinderseminar Queen's College 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.
 Wed, 13/02 10:30 Ben Green (Oxford) -- Queen's Lecture C Algebra Kinderseminar Queen's College 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.
 Wed, 06/02 10:30 Elisabeth Fink -- Queen's Lecture C Algebra Kinderseminar Queen's College 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  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.
 Wed, 30/01 10:30 Henry Bradford -- Queen's Lecture C Algebra Kinderseminar Queen's College 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”.
 Wed, 23/01 10:30 Martin Palmer -- Queen's Lecture C Algebra Kinderseminar Queen's College 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.
 Wed, 16/01 10:30 Alejandra Garrido -- Queen's Lecture C Algebra Kinderseminar Queen's College
 Wed, 24/10/2012 11:00 John Mackay -- St Hugh's, 80WR18 Algebra Kinderseminar
 Wed, 17/10/2012 11:00 Alejandra Garrido Angulo -- St Hugh's, 80WR18 ((Oxford University))) Algebra Kinderseminar I will give a brief report on some the topics discussed at the workshop "Golod-Shafarevich groups and rank gradient" that took place this August in Vienna. I will focus on results involving rank gradient.
 Wed, 23/05/2012 11:30 Dawid Kielak Algebra Kinderseminar
 Wed, 16/05/2012 11:30 Martin Bridson Algebra Kinderseminar
 Wed, 07/03/2012 11:30 Elisabeth Fink (Oxford) Algebra Kinderseminar
 Wed, 22/02/2012 11:30 \$\Pi\$eter Neumann (Oxford) Algebra Kinderseminar
 Wed, 15/02/2012 00:00 Jason Semeraro (Oxford) Algebra Kinderseminar Saturated fusion systems are a relatively new class of objects that are often described as the correct 'axiomatisation' of certain p-local phenomena in algebraic topology. Despite these geometric beginnings however, their structure is sufficiently rigid to afford its own local theory which in some sense mimics the local theory of finite groups. In this talk, I will briefly motivate the definition of a saturated fusion system and discuss a remarkable result of Michael Aschbacher which proves that centralisers of normal subsystems of a saturated fusion system, F, exist and are themselves saturated. I will then attempt to justify his definition in the case where F is non-exotic by appealing to some classical group theoretic results. If time permits I will speculate about a topological characterisation of the centraliser as the set of homotopy fixed points of a certain action on the classifying space of F.
 Wed, 08/02/2012 11:30 Tom Sutherland Algebra Kinderseminar