# Research Seminars: Geometry and Topology

Past Geometry and Topology:

## Fall 2017

**Time & Location**: All talks are on Thursday in Gibson Hall 414 at 12:30 PM unless otherwise noted.

**Organizer**: Slawomir Kwasik

*September 5*

**Organizational meeting**

Slawomir Kwasik - Tulane University
**Abstract**: *TBA*

*September 14*

**Whitehead torsion of inertial h-cobordisms**

Prof. Slawomir Kwasik - Tulane University
**Abstract**:

*The notions of an h-cobordism and the Whitehead torsion will be discussed. Some old and new results will be presented together with various open problems and conjectures.*

*September 21*

**Whitehead torsion of inertial h-cobordisms Part 2**

Prof. Slawomir Kwasik - Tulane University
**Abstract**:

*The notions of an h-cobordism and the Whitehead torsion will be discussed. Some old and new results will be presented together with various open problems and conjectures.*

*September 28*

**Discrete Morse Theory**

Fang Sun - Tulane University
**Abstract**:

*Discrete Morse Theory is a combinatorial adaption of the (smooth) Morse Theory developed by Robin Forman. The theory has various applications in applied and computational mathematics, as well as group theory.*

*October 5*

## Geometry and Topology

**Topology of representation spaces and invariants of finite reflection groups**

Mentor Stafa - Tulane University
**Abstract**:

*In this talk we will introduce the space of representations of a finitely generated discrete group into a compact and connected Lie group. We will study the rational cohomology of these spaces and their relation to the invariant theory of finite reflection groups.*

*October 19*

## Geometry and Topology

**The classifying space of transitionally commutative O(2)-bundles**

Bernardo Villarreal - Indiana University Purdue University Indianapolis
**Abstract**:

*In this talk I will define the space BcomG arising from commuting tuples in G originally defined by A. Adem and J. Gomez. This space sits inside the classifying space BG and I will focus on describing the space BcomO(2) via its mod 2 cohomology ring and the homotopy type of the homotopy fiber of the inclusion BcomO(2) into BO(2), denoted EcomO(2). It turns out that the mod 2 cohomology ring of BO(2) is a subring of the corresponding ring for BcomO(2) and that EcomO(2) is a wedge of spheres. This is joint work with O. Antolin and S. Gritschacher.*

*Date*

**Topic**

Speaker - Institution
**Abstract**: *TBA*

*Date*

**Topic**

Speaker - Institution
**Abstract**: *TBA*