MenuEvents for 04/21/2023 from all calendars
Algebra and Combinatorics Seminar
Time: 12:40PM - 1:40PM
Location: BLOC 302
Speaker: Jesus de Loera, University of California, Davis
Title: Who discovered Ramsey theory? An algebraic re-examination of Ramsey theory.
Abstract: This will be a combined event with the Colloquium.
Colloquium
Time: 12:40PM - 1:40PM
Location: BLOC 302
Speaker: Jesus De Loera, University of California, Davis
Description: Title: Who discovered Ramsey theory? An algebraic re-examination of Ramsey theory.
Abstract: It is indisputable Ramsey numbers are among the most mysterious and fascinating in Combinatorics. My talk focuses on Arithmetic Ramsey numbers and Diophantine problems, I discuss Rado numbers. These numbers are actually older than the usual graph theory version. For a positive integer k and linear equation E the Rado number R_k(E) is the smallest integer number n such that every k-coloring of [n] it contains a monochromatic solution to the equation E. A very famous example are Schur numbers, which are the Rado numbers for the equation E (X+Y=Z). I will discuss computation, bounds, and verification of Rado numbers and the fascinating history of Ramsey theory connected with names like Hilbert, Schur, van der Waerden, appearing along the way. I will not assume you know anything from the audience but I hope I will show, not just history, but also some new algebraic results. Our work combines discrete geometry, logic, algebraic geometry, an combinatorial number theory to investigate the behavior of Rado numbers. First, we computed many new exact values for Rado numbers using SAT solvers. In particular, we give a method for computing infinite families of Rado numbers, solving a few open questions. Regarding complexity and verification: Suppose someone suggests to you the value of R_k(E) . How can you certify that this value is correct and not a lie? We encode the problem as a system of polynomial equations and show that the degrees of Nullstellensatz certificates are actually bounded above by another Ramsey-number arising in a two-player game. The extremal k-colorings are in fact the solutions of this system which says that any proof that the proposed value of R_k(E) is not correct may require a doubly exponential certificate. At the heart is how combinatorial algebraic geometry relates to Ramsey numbers. This is joint work with Jack Wesley.
Mathematical Physics and Harmonic Analysis Seminar
Time: 1:50PM - 2:50PM
Location: BLOC 302
Speaker: Ruoyu Wang, Northwestern University
Title: Damped waves with singular damping on manifolds
Abstract: We will discuss a new damped wave semigroup for damping exhibiting H\”{o}lder-type blowup near a hypersurface of a compact manifold. We will use this semigroup to prove a sharp energy decay result for singular damping on the torus, where the optimal rate of energy decay explicitly depends on the singularity of the damping. We also show that no finite time extinction could happen under this setting. This is a joint work with Perry Kleinhenz.
Free Probability and Operators
Time: 4:00PM - 5:00PM
Location: BLOC 306
Speaker: Michael Anshelevich, TAMU
Title: Types of noncommutative independence and asymptotics of random matrices.
Abstract: We will discuss how the asymptotic joint distribution of two random matrices "in a general position" can be described using cyclic c-freeness and its particular cases; or, conversely, how different types of noncommutative independence can be asymptotically modeled by random matrices. In the first talk we will concentrate on algebraic independence theories; in the second and third talks, we will explain the connection with random matrices. The talks are based primarily on the articles arXiv:2207.06249 by Cébron and Gilliers; and arXiv:2205.01926 by Cébron, Dahlqvist, and Gabriel.
