Past Junior Topology and Group Theory Seminar

19 October 2016
16:00
Claudio Llosa Isenrich
Abstract

A Kähler group is a group which can be realised as the fundamental group of a close Kähler manifold. We will prove that for a Kähler group $G$ we have that $G$ is residually free if and only if $G$ is a full subdirect product of a free abelian group and finitely many closed hyperbolic surface groups. We will then address Delzant-Gromov's question of which subgroups of direct products of surface groups are Kähler: We explain how to construct subgroups of direct products of surface groups which have even first Betti number but are not Kähler. All relevant notions will be explained in the talk.

  • Junior Topology and Group Theory Seminar
8 June 2016
16:00
Claudio Llosa Isenrich
Abstract

We will explain a result of Bridson, Howie, Miller and Short on the finiteness properties of subgroups of direct products of surface groups. More precisely, we will show that a subgroup of a direct product of n surface groups is of finiteness type $FP_n$ if and only if there is virtually a direct product of at most n finitely generated surface groups. All relevant notions will be explained in the talk.

 

  • Junior Topology and Group Theory Seminar
25 May 2016
16:00
Kobert Ropholler
Abstract

The simplicial boundary is another way to study the boundary of CAT(0) cube complexes. I will define this boundary introducing the relevant terminology from CAT(0) cube complexes along the way. There will be many examples and many pictures, hopefully to help understanding but also to improve my (not so great) drawing skills. 

  • Junior Topology and Group Theory Seminar
18 May 2016
16:00
Gareth Wilkes
Abstract

I will discuss the circumstances in which residual finiteness properties of an amalgamated free product $A\ast_c B$ may be deduced from the properties of $A$ and $B$, with particular regard to the pro-p residual properties.

  • Junior Topology and Group Theory Seminar
11 May 2016
16:00
Nicolaus Heuer
Abstract

Quasimorphisms (QM) of groups to the reals are well studied and are linked to stable commutator length (scl) via Bavard Duality- Theorem. The notion of QM can be generalized to yield maps  between groups such that each QM from one group pulls back to a QM in the other.

We will give both a short overview of features of scl and investigate these generalized QMs with large scale properties of the commutator group. 

  • Junior Topology and Group Theory Seminar
4 May 2016
16:00
Alex Margolis
Abstract

In his ICM address in 1983, Gromov proposed a program of classifying finitely generated groups up to quasi-isometry. One way of approaching this is by breaking a group down into simpler parts by means of a JSJ decomposition. I will give a survey of various JSJ theories and related quasi-isometric rigidity results, including recent work by Cashen and Martin.

  • Junior Topology and Group Theory Seminar
9 March 2016
16:00
Renee Hoekzema
Abstract

Orientable manifolds can only have an odd Euler characteristic in dimensions divisible by 4. I will prove the analogous result for spin and string manifolds, where the dimension can only be a multiple of 8 and 16 respectively. The talk will require very little background. I'll go over the definition of spin and string structures, discuss cohomology operations and Poincare duality.

  • Junior Topology and Group Theory Seminar

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