VT Mathematics Colloquium

Fridays 4:00-5:00 PM Eastern Time

McBryde 455

February 7, 2025

Speaker: Dr. Paata Ivanisvili (UC Irvine)

Title: Discrete approximation theory

I will discuss polynomial approximation problems on the n-dimensional hypercube, focusing on quantitative estimates of the approximation error as n grows. This topic represents a burgeoning area in the analysis of Boolean functions—one that is far less understood than its classical counterpart on the real line. I will present several recent results together with its applications, as well as highlight ongoing challenges and open problems in the field.
February 14, 2025

Speaker: Dr. Luis Núñez-Betancourt (CIMAT)

Title: Singularities of Polynomials with Square-Free Support

A polynomial over a field is square-free supported if every variable appearing in it has degree at most one. Interest in such polynomials arises from matroid support polynomials, studied by Bath and Walther. In this talk, we will provide an overview of the study of singularities in prime characteristic via the Frobenius map. We will show that the algebraic variety defined by an irreducible polynomial with square-free support has mild singularities, answering a question posed by Bath, Mustață, and Walther. We will also discuss the consequences of these results, including their implications in characteristic zero.
February 28, 2025

Speaker: Dr. Jake Fillman (Texas A&M)

Title: Schrödinger operators with thin spectra

The Schrödinger equation is the foundational equation of nonrelativistic quantum mechanics. Studying the time-independent part leads to the eigenvalue equation of a Schrödinger operator, whose spectra contain a wealth of information about the underlying quantum system. We will survey some results about Schrödinger operators having exotic properties, such as spectra that can be "thin" Cantor sets.
March 21, 2025

Speaker: Dr. Phan Thành Nam (LMU Munich)

Title: Isoperimetric Inequalities and Binding Problems in Atomic Physics

I will discuss the connection between the classical isoperimetric inequality and the critical mass problem in nuclear fission, which is described by the liquid drop model. Techniques developed for this problem are also helpful in establishing certain universality results for large atoms, particularly in relation to the ionization problem in quantum physics: How many electrons can a nucleus bind?
March 28, 2025

Speaker: TBD

Title: TBD

April 4, 2025

Speaker: Dr. Alexander Barg (U Maryland)

Title: TBD

April 11, 2025

Speaker: Dr. Ken Ono (University of Virginia)

Title: TBD

April 18, 2025

Speaker: Dr. Kreso Josic (University of Houston)

Title: TBD

April 25, 2025

Speaker: TBD

Title: TBD

May 2, 2025

Speaker: Dr. Benjamin Peherstorfer (New York University)

Title: TBD