05C50 Online Seminar: Hajime Tanaka

In this talk, I will discuss certain extremal configurations in Q-polynomial distance-regular graphs (or P- and Q-polynomial association schemes), which we call descendents. The descendents of a hypercube are precisely its faces. I will show how they arise naturally and play a role in various topics, such as the Erdős-Ko-Rado theorems, the Assmus-Mattson theorems, orthogonal (Laurent) polynomials, and Ambainis' quantum algorithm for the element distinctness problem (if time allows). As algebraic tools, I will mention two matrix algebras, the (commutative) Bose-Mesner algebra and the (noncommutative) Terwilliger algebra.

A recording of the talk will be shared on this website. You may email the speaker for their slides.