VT Mathematics Colloquium

Fridays 4:00-5:00 PM Eastern Time

McBryde 455

February 7, 2025

Speaker: 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: 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: 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: 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

Location: 113 McBryde

Speaker: Lillian Pierce (Duke)

Title: Superorthogonality

How do we check if two vectors are orthogonal? We compute their dot product, which by definition takes two vectors as inputs. How do we check if two functions are orthogonal? We compute their inner product, which by definition takes two functions as inputs. Why only two? What would it mean for 4 functions to be “orthogonal”? Or 8 functions? Or 7 functions? Let’s call this superorthogonality. What can we deduce about collections of functions that are superorthogonal? In this accessible talk, we will explore how accidental encounters with papers spanning 90 years led to a systematic investigation of these questions, and a way to see that previously “unrelated” theorems in harmonic analysis and number theory share a very interesting structure deep under their surface.
April 4, 2025

Speaker: Alexander Barg (U Maryland)

Title: Classical and quantum codes on Coxeter groups

Classical Reed-Muller codes form a well-known family of binary codes on the cubical complex, which also gives rise to a family of quantum codes. In the first part of the talk we extend the construction of the classical RM family to binary codes defined on an arbitrary finite Coxeter complex and establish basic properties of the new code class. In the second part we present a geometric description of a set of transversal logical operators of quantum RM codes. The talk assumes no background in coding theory or quantum computations, developing the constructions from the first principles. We will define classical and quantum codes and discuss the motivation for the construction of their logical operators. Based on joint works with Nolan Coble, Dominik Hangleiter, and Christopher Kang.
April 11, 2025

Speaker: Ken Ono (University of Virginia)

Title: TBD

April 18, 2025

Speaker: Kreso Josic (University of Houston)

Title: TBD

April 25, 2025

Speaker: TBD

Title: TBD

May 2, 2025

Speaker: Benjamin Peherstorfer (New York University)

Title: TBD