Events for 02/02/2024 from all calendars

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Youngho Yoo, TAMU

Title: Minimum degree conditions for apex-outerplanar minors

Abstract: Motivated by Hadwiger's conjecture, we study graphs H for which every graph with minimum degree at least |V(H)|-1 contains H as a minor. We prove that a large class of apex-outerplanar graphs satisfies this property. Our result gives the first examples of such graphs whose vertex cover numbers are significantly larger than a half of its vertices, and recovers all known such graphs that have arbitrarily large maximum degree. Our proof can be adapted to directed graphs to show that every directed graph with minimum out-degree at least t contains a certain orientation of the wheel and of every apex-tree on t+1 vertices as a subdivision and a butterfly minor respectively. Joint work with Chun-Hung Liu.

Integrable probability: Random matrices at high and low temperatures

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Vadim Gorin

Description: We will start from a brief overview of what integrable probability is and then discuss a random matrix problem. Suppose that you are given self-adjoint matrices A and B with known eigenvalues and unknown eigenvectors. What can you say about eigenvalues of C=A+B? It took the entire 20th century to obtain deterministic characterizations of the eigenvalues in the work of Weyl, Horn, Klyachko, and Knutson-Tao. In the talk we will discuss the probabilistic version of the problem, in which A and B are random and an important role is played by the random matrix parameter Beta, that takes values 1, 2, or 4, depending on whether we deal with real, complex, or quaternionic matrices. I will explain how this parameter can be taken to be an arbitrary positive real number (identified with the inverse temperature in the terminology of the statistical mechanics) and outline a rich asymptotic theory as Beta tends to zero and to infinity.