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Seminars and Colloquiums
for the week of September 17, 2018


Jerzy Dydak, University of Tennessee
David Jensen, University of Kentucky

Ryan Unger, University of Tennessee
Ken Stephenson, University of Tennessee
Long Chen, University of California, Irvine
Olivia Prosper, University of Kentucky
Peter McGrath, University of Pennsylvania
Luc Doyen, University of Bordeaux
Vasileios Maroulas, University of Tennessee

3:00 PM – 3:30 PM
Monday, Tuesday, & Wednesday
Room: Ayres 401
Hosted by: Maggie Wieczorek
Topics: How to get involved in the Mathematics Department; Math Graduate Student Council (MGSC) role in the Mathematics Department; MGSC past accomplishments.

Monday, 9/17

TITLE: Compactifications via ultrafilters II
SPEAKER: Jerzy Dydak, University of Tennessee
TIME: 3:35 PM-4:25 PM
ROOM: Ayres 406
I will discuss constructing compactifications using ultrafilters and applying the following result from the book "Geometric group theory" (Cornelia Drutu and Michael Kapovich):

Lemma 1.18. [Extension lemma] Suppose that X,Y topological spaces, where Y is regular and X contains a dense subset A.

1. If f : X to Y is a mapping satisfying the property that for each x in X the restriction of f to A union {x} is continuous, then f is continuous.

2. Assume now that A isopen and setX\A=Z. Suppose that f:X to Y is such that the restriction f|A union {z} is continuous at z for every point z in Z. Then f:X to Y is continuous at each point z of Z.

A proof of the lemma will be presented

TITLE: Linear Systems on General Curves of Fixed Gonality
SPEAKER: David Jensen, University of Kentucky
TIME: 3:35 PM-4:25 PM
ROOM: Ayres 113
The geometry of an algebraic curve is governed by its linear systems. While many curves exhibit bizarre and pathological linear systems, the general curve does not. This is a consequence of the Brill-Noether theorem, which says that the space of linear systems of given degree and rank on a general curve has dimension equal to its expected dimension. In this talk, we will discuss a generalization of this theorem to general curves of fixed gonality. To prove this result, we use tropical and combinatorial methods. This is joint work with Dhruv Ranganathan, based on prior work of Nathan Pflueger.

Tuesday, 9/18

TITLE: Colding-Minicozzi Paper 2-part 2
SPEAKER: Ryan Unger, University of Tennessee
TIME: 4:00 PM-5:30 PM
ROOM: Ayres 121
We will show curvature estimates on embedded minimal disks with bounded total curvature.

Wednesday, 9/19

TITLE: Projective Structures, beginning with Affine Tori
SPEAKER: Ken Stephenson, University of Tennessee
TIME: 2:30 PM-3:20 PM
ROOM: Ayres 113
(Joint with former student Chris Sass) I will introduce some of the basics concerning circle packing in the setting of triangulated tori, beginning with a new proof of existence and uniqueness. Such circle packings provide one type of projective structure. However, our methods can be extended to provide more general affine structures --- in fact, for any triangulation, we obtain a full smoothly parameterized family of affine structures.

TITLE: Convergence Proof of FAS for Nonlinear Problems
SPEAKER: Long Chen, University of California, Irvine
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 113
Full Approximation Scheme (FAS) is a widely used multigrid method for nonlinear problems. In this talk, we shall provide a new framework to analyze FAS for convex optimization problems and improve the original method. We view FAS as an inexact version of nonlinear multigrid methods based on space decomposition and subspace correction.

The local problem in each subspace can be simplified to be a linear and one gradient decent iteration is enough to ensure a linear convergence.

This is a joint work with Steve Wise (University of Tennessee) and Xiaozhe Hu (Tuffs University).

Thursday, 9/20

TITLE: A stochastic model for the generation of Plasmodium falciparum parasite diversity
SPEAKER: Olivia Prosper, University of Kentucky
TIME: 2:10 PM-3:10 PM
ROOM: Ayres 405
The malaria parasite Plasmodium falciparum requires a vertebrate host, such as a human, and a vector host, the Anopheles mosquito, to complete a full life cycle, with sexual reproduction occurring in the vector host. This sexual stage of the parasite life cycle creates opportunities for the production of genetically novel parasites. In the meantime, a mosquito’s biology creates bottlenecks in the infecting parasites’ development. We constructed a two-stage stochastic model to better understand the role of mosquito biology in mediating the generation of parasite diversity. The first stage is a stochastic model of parasite development within the mosquito, and the second is a model of sequence diversity generation via reassortment and recombination. Despite the bottlenecks, our framework shows that the possibility for reassortment and recombination ultimately increases the diversity of the parasite population within the mosquito at the sporozoite stage, the stage in which parasites are transmissible to humans. In fact, if the initial blood meal entering the mosquito is composed of only two parasite genotypes, the probability that more than two unique genotypes is transmitted from the mosquito to a human is over 50% for a wide range of initial gametocyte densities.

TITLE: Existence and Uniqueness for Free Boundary Minimal Surfaces
SPEAKER: Peter McGrath, University of Pennsylvania
TIME: 4:00 PM-5:00 PM
ROOM: Ayres 121
Let B^3 be the unit ball in R^3 and consider the family of surfaces contained in B^3 with boundary on the unit sphere S^2. The critical points of the area functional amongst this class are called Free Boundary Minimal Surfaces. The latter surfaces are physically realized by soap films in equilibrium and have been the subject of intense study. In the 1980s, it was proved that flat equatorial disks are the only free boundary minimal surfaces with the topology of a disk. It is conjectured that a surface called the critical catenoid is the unique (up to ambient rotations) embedded free boundary minimal annulus. I will discuss some recent progress towards resolving this conjecture. I will also discuss some sharp bounds (Joint work with Brian Freidin) for the areas of free boundary minimal surfaces in positively curved geodesic balls which extend works of Fraser-Schoen and Brendle in the Euclidean setting.

Friday, 9/21

TITLE: Viability and control for ecology-economic models
SPEAKER: Luc Doyen, University of Bordeaux
TIME: 10:10 AM-11:00 AM
ROOM: Ayres 401

TITLE: Statistics, Topology and Data Analysis
SPEAKER: Vasileios Maroulas, University of Tennessee
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 405
In this talk, I will present methods of topological data analysis engaged with statistics for solving data problems. As a paradigm, I will discuss supervised learning, and a new classification approach will be presented using a metric that accounts for changes in persistence and cardinality. I will benchmark several classification results using real data provided by the US Army Research Lab. Last, I will present a way for quantifying uncertainty by estimating distributions of persistence diagrams, a topological summary. 


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:

Sept. 10, 2018

Sept. 3, 2018

Aug. 27, 2018



last updated: September 2018

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