Past 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
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.

  • Junior Topology and Group Theory Seminar
20 January 2016
16:00
Federico Vigolo
Abstract

I will illustrate how to build families of expanders out of 'very mixing' actions on measure spaces. I will then define the warped cones and show how these metric spaces are strictly related with those expanders.

  • Junior Topology and Group Theory Seminar

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