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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.


October 26

Geometry and Topology

Topological and Geometric Reconstruction of Metric Graphs


Sushovan Majhi - Tulane University

Abstract:

In the last decade, estimation of topological and geometric features of an unknown underlying space from a finite sample has received an increasing attention in the field of computational topology and geometry. For example, recently a reconstruction guarantee for the topology of an embedded smooth n-manifold from a finite cover by balls of sufficiently small radius around a dense enough finite  sample is proved. Random sampling and probabilistic estimates are also considered along with the deterministic case. These estimates imply that with increasing sample size, the probability of reconstructing the underlying space tends to 1, thus we can recover the space almost surely as the sample size increases to infinity. Not all spaces are smooth manifolds. In practice, non-smooth manifolds or even non-manifolds are often of interest. We shall address the reconstruction problems for these spaces. Also, we touch upon our recent development on the reconstruction of a special type of embedded topological spaces called metric graphs.


November 2

Topic


Rafał Komendarczyk - Tulane University

Abstract: I will discuss progress towards defining asymptotic higher linking numbers for divergence-free vector fields.


December 7

Simplicial approximations and homology with local coefficients


Fang Sun - Tulane University

Abstract:

We will apply two types of simplicial approximations to tackle some problems in homology and cohomology with local coefficients.


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Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 math@math.tulane.edu