Seminars and Colloquiums
for the week of May 1, 2017
Alexandre Karassev, Nipissing University, Ontario (Canada)
Robert Schneider, Emory University
Joshua Mike, UTK
Monday, May 1st
TOPOLOGY/ GEOMETRY SEMINAR
Title: The Bing-Borsuk conjecture: search for a counterexample
Speaker: Alexandre Karassev, Nipissing University, Ontario (Canada)
Time: 2:00p - 2:50p
Room: Ayres 110
The Bing-Borsuk conjecture states that any homogeneous compact finite-dimensional ANR must be a manifold. I will present an overview of various results related to this conjecture. Next, I will discuss possible approaches to construct a counterexample.
ORAL SPECIALTY EXAM
Speaker: Pawel Grzegrzolka
Time: 1:00p - 1:50p
Room: Ayres 110
During the past several years, coarse spaces (especially coarse metric spaces) have been studied by a large number of mathematicians due to the close connections to conjectures concerning C-star algebras, K-theory, topological rigidity and others. We begin this talk by introducing basic definitions concerning coarse metric spaces, including equivalent definitions of uniformly expansive and effectively proper functions. After discussing the category of coarse metric spaces, we will try to generalize previously defined notions to families of metric spaces as well as to non-metric coarse spaces. Then, we will introduce well-known properties of coarse metric spaces, including finite asymptotic dimension, exactness, and coarse embeddability, and we will apply their definitions to metric families/standard total spaces. Finally, we will investigate primitive permanence results for families of metric spaces and examine permanence properties of finite asymptotic dimension and exactness. This talk is based on Erik Guentner’s paper "Permanence in coarse geometry."
Committee: Nikolay Brodskiy, Jerzy Dydak (chair), Morwen Thistlethwaite
Title: Partition Zeta Functions
Speaker: Robert Schneider, Emory University
Time: 3:35p - 4:25p
Room: Ayres 113
In this talk we will highlight partition-theoretic analogies to multiplicative number theory. We use sums over integer partitions to compute the values of constants such as π via partition-theoretic analogs of the Riemann zeta function and other objects from classical number theory, and to discuss q-series whose limiting values are the arithmetic densities of certain subsets of natural numbers, such as the square-free integers whose density is well known to correspond to .
Thursday, May 4th
PhD THESIS DEFENSE
Title: Statistical Computational Topology and Geometry for Understanding Data
Speaker: Joshua Mike, UTK
Time: 10:10a - 11:10a
Room: Ayres G004
In this defense, I will describe three projects involving data analysis which focus on engaging statisitics with the geometry and/or topology of the data. These projects show the range of data analysis from application of a known technique to new data to the development of new techniques and new viewpoints in the subject.
The first project involves the development and implementation of kernel density estimation for persistence diagrams. These kernel densities consider neighborhoods for every feature in the center diagram and gives to each feature an independent, orthogonal direction. The creation of kernel densities in this realm yields a (previously unavailable) full characterization of the (random) geometry of a dataspace or data distribution.
In the second project, cohomology is used to guide a search for kidney exchange cycles within a kidney paired donation pool. The same technique also produces a score function that helps to predict a patient-donor pair's a priori advantage within a donation pool.
The resulting allocation of cycles is determined to be equitable according to a strict analysis of the allocation distribution.
In the last project, a previously formulated metric between surfaces called continuous Procrustes distance (CPD) is applied to species discrimination in fossils. This project involves both the application and a rigorous comparison of the metric with its primary competitor, discrete Procrustes distance. Besides comparing the separation power of discrete and continuous Procrustes distances, the effect of surface resolution on CPD is investigated in this study. Committee members are: Vasileios Maroulas (Chair), Conrad Plaut, Ken Stephenson, Mike Berry
If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.
If you have questions, or a date you would like to confirm, please contact colloquium AT math DOT utk DOT edu
3/13/17 - Spring Break