Colloquium 04/10: Lizzy Huang on Harmonic Maps with Repulsive Potentials

As part of the R.W. Yeagy Colloquium Series, on Monday, April 10 at 2:30pm in Math Building 357, Lizzy Huang will speak on Harmonic Maps with Repulsive Potentials.

Abstract: Many questions in topology and physics can be expressed in terms of finding a function f  between a curved space M (the domain) and another curved space N (the target) which minimizes a natural energy functional: \int_M |df|^2. Functions that minimize this energy are called harmonic maps. One method to obtain a harmonic map is to consider a family of maps  which follow a path of ‘steepest descent’. In this talk, I will discuss a modification of this approach in which an unbounded potential energy is added to the total energy. Then I will discuss the behavior and singularities of the limiting maps in cases of special significance to topology. I will only assume knowledge of multivariable calculus and linear algebra for this talk.

Colloquium 04/07: Dr. David Lax on “An Order Filter Model for the Algebraic Relations Defining the Grassmannian and its Cousins”

As part of the R.W. Yeagy Colloquium Series, Dr. David Lax will be speaking at 1:30pm on Friday, April 7 in Math Building 357 on An Order Filter Model for the Algebraic Relations Defining the Grassmannian and its Cousins.

Abstract: The Grassmann manifolds consist of planes in a vector space and have coordinates given by determinants. These coordinates are naturally partially ordered, and the relations among the coordinates are straightening laws–meaning they respect this order.  For any of the Grassmann manifolds’ cousins, the ‘minuscule flag manifolds,’ we present a model for its coordinates that uses colored partially ordered sets and some straightening laws shared by these coordinates.

Colloquium 3/8: Ryan Jensen on Topological Data Analysis

On Thursday March 9th at 2 PM in Math Building 357, Ryan Jensen from the University of Tennessee will be talking about “Topological Data Analysis”.

Abstract: What is the shape of the following collection of data points (original image from Persistence Theory: From Quiver Representations to Data Analysis by Steve Y. Oudot)?


It depends on the “scale” from which the points are viewed. From a very small scale, all that is visible is a point; from a larger scale, there are multiple “B’s”; at an even larger scale, an “A” appears; finally, when viewed from a great distance, there is nothing but a blob.

In this talk we will give an introduction (accessible to undergraduates) to persistent homology, which is a tool from algebraic topology used to study the shape (homology) of data and through which scales that shape persists. We will look at the persistent homology of the above example as well as real life examples, including the shape of protein distribution in medicated cells. Finally, we will briefly discuss new results from large scale geometry which could be useful in determining other persistent properties of a data set.

Colloquium 03/06: Travis Russell on “Abstract Characterizations in Operator Theory and Some Applications”

On Monday March 6th from 2:30-3:30 PM in Math 357, Travis Russell from the University of Nebraska will be talking about “Abstract Characterizations in Operator Theory and Some Applications.”

Abstract characterizations occur frequently in mathematics. Roughly speaking, an abstract characterization is a way of extracting the essential structure of a mathematical object that normally exists in a highly structured and complex setting. In this talk, I will provide an overview of some abstract characterizations that occur in the theory of operator spaces. I will illustrate how quantum physics has motivated some of these ideas and how these ideas are now contributing to the theory of quantum computation. (Flyer in PDF form)

Colloquium 2/27: Quinn Morris on “From Theory to Practice: Boundary Value Problems and Prokelesia Arginata”

As part the R.W. Yeagy Colloquium Series, Mr. Quinn Morris will be talking about “FROM THEORY TO  PRACTICE: BOUNDARY VALUE PROBLEMS AND PROKELISIA ARGINATA at 2:30 PM on Monday February 27th in Math 357.

Abstract: In a first course in ordinary differential equations, one often treats initial value problems and is able to show existence & uniqueness of solutions when f is “nice”. In this talk, we will instead consider boundary value problems, and observe that even for very “nice” functions f, existence and uniqueness is a much more complicated question. In the second half of the talk, we will discuss some boundary value problems arising from population models with density dependent dispersal on the boundary. The NSF-funded study of these models is on-going work with a group of undergraduates, graduate students, and faculty at three universities. (flyer in PDF form)

Colloquium 01/30: Dr. Kirsti Wash on My Experience with Student Research

As part of the R. W. Yeagy Colloquium Series, on January 30, 2017, at 3:10 pm in Math Building 357 (please note the time!), Dr. Kirsti Wash of Trinity College will be presenting two talks. The second of which is entitled My Experience with Student Research.

Abstract: Over the past four years, I have advised 7 undergraduate research students and 2 student senior theses. Although the mathematical background varied greatly among each student, I consider each project undertaken a success. In this talk, I will discuss my experience in advising undergraduate research. In particular, I will discuss the difficulties I have faced in judging a student’s research capabilities, in choosing appropriate problems, and in leading them through the writing process.

Colloquium 01/30: Dr. Kirsti Wash on The Packing Chromatic Number of Subdivisions of Subcubic Graphs

As part of the R. W. Yeagy Colloquium Series, on January 30, 2017, at 2:30 pm in Math Building 357 (please note the time!), Dr. Kirsti Wash of Trinity College will be presenting two talks. The first of which is entitled The Packing Chromatic Number of Subdivisions of Subcubic Graphs.

Abstract: The packing chromatic number \chi_\rho(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into sets X_1, \ldots, X_k where X_i is an i-packing for each i\in\{1,2,\ldots,k\}. Gastineau and Togni recently conjectured that \chi_\rho(S(G))< 5 where S(G) is the subdivision of any subcubic graph. We show that the conjecture is indeed true for all generalized prisms of a cycle other than the Petersen graph. We also give a more general class of 2-connected subcubic graphs for which the conjecture holds and discuss the obstacles of proving the conjecture in general. This is joint work with Bostjan Bresar, Sandi Klavzar, and Douglas F. Rall.