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Seminars and Colloquiums
for the week of October 22, 2018


Brendon LaBuz, Saint Francis University

Chris Oballe, University of Tennessee
Mat Langford, University of Tennessee
Ming-Jun Lai, University of Georgia
Noah Giansiracusa, Swarthmore College
Rafael Montezuma, Princeton University
Noah Giansiracusa, Swarthmore College

Cancelled for this week

Monday, 10/22

TITLE: The fundamental group of the Hawaiian earring
SPEAKER: Brendon LaBuz, Saint Francis University
TIME: 3:35 PM-4:25 PM
ROOM: Ayres 406
The Hawaiian earring is the metric wedge of a null sequence of circles. Its fundamental group is interesting since a loop in the Hawaiian earring can traverse infinitely many of the circles. Its fundamental group can be described using infinitely many generators (each representing a loop around one of the circles), infinite (transfinite) words, and infinite cancellation. In their paper The combinatorial structure of the Hawaiian earring group, Cannon and Conner give such a description. Their theory is developed in the generalized setting of big free groups for a generating set of arbitrary cardinality. We will treat their theory and their nice proof that each equivalence class of transfinite words contains a unique reduced word.

The Cayley graph of a free group is a tree and the free group acts isometrically on the tree. Cannon and Conner define a big Cayley graph of their big free groups. We will discuss how big free groups can be considered to act big isometrically on their big Cayley graph, and to what extend the big Cayley graph is a big tree.

Tuesday, 10/23

TITLE: Bayesian Inference for Persistence Diagrams using Marked Poisson Processes
SPEAKER: Chris Oballe, University of Tennessee
TIME: 2:10 PM-3:10 PM
ROOM: Ayres 113
After a brief overview of persistent homology and its accompanying statistical methods, I'll present a point process model for persistence diagrams that naturally yields a Bayesian theory. Specifically, persistence diagrams are thought of as marked Poisson processes, and this formulation is used to construct an unbiased estimator of the posterior intensity. I'll outline an implementation of the theory that relies on mixed Gaussian assumptions. Finally, I'll use a score based on posterior intensities to classify simulated data.

TITLE: Colding and Minicozzi paper I section II: Estimates for stable annuli with slits
SPEAKER: Mat Langford, University of Tennessee
TIME: 3:30 PM-5:30 PM (note change)
ROOM: Ayres 121
This is a continuation from last week. We will show that certain stable minimal disks which are multivalued graphs can be extended 'horizontally'.

Wednesday, 10/24

TITLE: Bivariate Spline Solutions to the Helmholtz Equation with Large Wave Numbers
SPEAKER: Ming-Jun Lai, University of Georgia
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 113
Although there are many computational methods, e.g. hp finite element methods available, numerical solution of the Helmholtz equation with large wave number still poses a challenge. It is known there is a so-called pollute error which prevents an accurate solution from the current conventional methods.  We shall explain how to use bivariate splines to numerically solve the Helmholtz equation with large wave number, e.g. wave number k=1000 or larger. We will demonstrate numerically that the bivariate spline method enables us to find very accurate solution for large wave number, e.g., k=1500. No pollution phenomenon is observed in our numerical experiments. In addition, we shall establish the existence, uniqueness and stability of the weak solution to the Helmholtz equation under the assumption that k^2 is not an eigenvalue of Dirichlet boundary value problem of the Poisson equation. Under this assumption, the standard requirement of strictly star-shaped domain for the well-posedness of the Helmholtz equation is no longer needed. Finally, we will explain how to use bivariate splines to solve Helmholtz equation over exterior domain by using a PML technique.  Spline solution to Helmholtz equation with high frequency (>100)  over domain [-10,10]^2 can be found accurately. These show the efficiency and effectiveness of our bivariate spline functions.  

Thursday, 10/25

TITLE: Classifying Fingerprints with Persistent Homology
SPEAKER: Noah Giansiracusa, Swarthmore College
TIME: 2:10 PM-3:10 PM
ROOM: Ayres 405
Classifying fingerprints (dividing them into loops, whorls, arches, etc.) is a natural problem to apply topological methods to since these classes are independent of choice of coordinates. I’ll discuss joint work with Chul Moon where we apply persistent homology and perform basic machine learning feature selection in several different ways and compare the results.

TITLE: Extremal metrics for the min-max width
SPEAKER: Rafael Montezuma, Princeton University
TIME: 4:00 PM-5:00 PM
ROOM: Ayres 121
We present our study on the min-max width of Riemannian three-dimensional spheres. This is a natural geometric invariant which is closely related with critical values of the area functional acting on closed surfaces, and can be interpreted as the first eigenvalue of a non-linear spectrum of a Riemannian metric, as suggested by Gromov. We will focus first on optimal bounds for the above invariant involving their volumes in a fixed conformal classes. If time permits we will discuss some general properties of extremal metrics for the min-max width. This is all part of a joint work with Lucas Ambrozio.

Friday, 10/26

TITLE: Geometry of Supreme Court Voting
SPEAKER: Noah Giansiracusa, Swarthmore College
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 405
Political scientists and legal scholars have used various mathematical models and tools to help understand the behavior of the U.S. Supreme Court (and voting systems more generally).  These tend to range from probabilistic, to game theoretic, to geometric.  I'll present a quick look at some of these mathematical approaches to the Court including a couple recent attempts in which I have been involved.

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 mlangfo5 AT utk DOT edu

Past notices:

Oct. 15, 2018

Oct. 8, 2018

Oct. 1, 2018

Sept. 24, 2018

Sept. 17, 2018

Sept. 10, 2018

Sept. 3, 2018

Aug. 27, 2018



last updated: October 2018

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