Past Junior Topology and Group Theory Seminar

4 March 2015
15:00
Michal Ferov
Abstract

A group is called residually finite if every non-trivial element can be homomorphically mapped to a finite group such that the image is again non-trivial. Residually finite groups are interesting because quite a lot of information about them can be reconstructed from their finite quotients. Baumslag showed that if G is a finitely generated residually finite group then Aut(G) is also residually finite. Using a similar method Grossman showed that if G is a finitely generated conjugacy separable group with "nice" automorphisms then Out(G) is residually finite. The graph product is a group theoretic construction naturally generalising free and direct products in the category of groups. We show that if G is a finite graph product of finitely generated residually finite groups then Out(G) is residually finite (modulo some technical conditions)

  • Junior Topology and Group Theory Seminar
25 February 2015
16:00
Claudio Llosa Isenrich
Abstract

A Kähler group is a group which is isomorphic to the fundamental group of a compact Kähler manifold. In 2008 Dimca and Suciu proved that the groups which are both Kähler and isomorphic to the fundamental group of a closed 3-manifold are precisely the finite subgroups of $O(4)$ which act freely on $S^3$. In this talk we will explain Kotschick's proof of this result. On the 3-manifold side the main tools that will be used are the first Betti number and Poincare Duality and on the Kähler group side we will make use of the Albanese map and some basic results about Kähler groups. All relevant notions will be explained in the talk.

  • Junior Topology and Group Theory Seminar
18 February 2015
16:00
Alexander Margolis
Abstract

In Bass-Serre theory, one derives structural properties of groups from their actions on simplicial trees. In this talk, we introduce the theory of groups acting on $\mathbb{R}$-trees. In particular, we explain how the Rips machine is used to classify finitely generated groups which act freely on $\mathbb{R}$-trees.

  • Junior Topology and Group Theory Seminar
11 February 2015
16:00
Robert Kropholler
Abstract

I will look at some decidability questions for subgroups of Aut($F_n$) for general $n$. I will then discuss semisimple actions of Aut($F_n$) on complete CAT(0) spaces proving that the Nielsen moves will act elliptically. I will also look at proving Aut($F_3$) is large and if time permits discuss the fact that Aut($F_n$) is not Kähler

  • Junior Topology and Group Theory Seminar
4 February 2015
16:00
Gareth Wilkes
Abstract

This talk will give an almost complete proof of the h-cobordism theorem, paying special attention to the sources of the dimensional restrictions in the theorem. If time allows, the alterations needed to prove its cousin, the s-cobordism theorem, will also be sketched.

  • Junior Topology and Group Theory Seminar
28 January 2015
16:00
Henry Bradford
Abstract

The Nottingham Group of a finite field is an object of great interest in profinite group theory, owing to its extreme structural properties and the relative ease with which explicit computations can be made within it. In this talk I shall explore both of these themes, before describing some new work on efficient short-word approximation in the Nottingham Group, based on the profinite Solovay-Kitaev procedure. Time permitting, I shall give an application to the dynamics of compositions of random power series.

  • Junior Topology and Group Theory Seminar
21 January 2015
16:00
Abstract
Wilson type groups are the first known examples of hereditarily just infinite (h.j.i.) profinite groups which are not virtually pro-p. In this talk I will firstly present a short survey on just infinite groups and where h.j.i. groups appeared. Secondly I will present the construction of Wilson type groups via iterated wreath products and finally I will discuss results obtained in my PhD regarding the Hausdorff dimension and the subgroup growth of these groups.
  • Junior Topology and Group Theory Seminar
3 December 2014
16:00
Charles Cox
Abstract

Deciding whether or not two elements of a group are conjugate might seem like a trivial problem. However, there exist finitely presented groups where this problem is undecidable: there is no algorithm to output yes or no for any two elements chosen. In this talk Houghton groups (a family of groups all having solvable conjugacy problem) will be introduced as will the idea of twisted conjugacy: a generalisation of the conjugacy problem where an automorphism is also given. This will be our main tool in answering whether finite extensions and finite index subgroups of any Houghton group have solvable conjugacy problem.

  • Junior Topology and Group Theory Seminar
19 November 2014
16:00
Federico Vigolo
Abstract

In 1983 Kerckhoff settled a long standing conjecture by Nielsen proving that every finite subgroup of the mapping class group of a compact surface can be realized as a group of diffeomorphisms. An important consequence of this theorem is that one can now try to study subgroups of the mapping class group taking the quotient of the surface by these groups of diffeomorphisms. In this talk we will study quotients of surfaces under the action of a finite group to find bounds on the cardinality of such a group.

  • Junior Topology and Group Theory Seminar

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