15 June 2016
16:00
Past 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.
1 June 2016
16:00
Sam Brown
Abstract
I will describe a method to find negatively curved structures on some groups, by manipulating metrics on piecewise hyperbolic complexes. As an example, I will prove that hyperbolic limit groups are CAT(-1).
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.
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.
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.
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.
27 April 2016
16:00
Vigolo Federico
Abstract
in this talk I will try to introduce some key ideas and concepts about random walks on discrete spaces, with special interest on random walks on Cayley graphs.
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.
2 March 2016
16:00
Alex Margolis
Abstract
I will present a basic overview of finiteness conditions, group cohomology, and related quasi-isometry invariance results. In particular, I will show that if a group satisfies certain finiteness conditions, group cohomology with group ring coefficients encodes some structure of the `homology at infinity' of a group. This is seen for hyperbolic groups in the work of Bestvina-Mess, which relates the group cohomology to the Čech cohomology of the boundary.