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.
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.
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)
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)
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.