Student/Postdoc Working Geometry Seminar

Date: November 11, 2022

Time: 1:00PM - 2:15PM

Location: BLOC 628

Speaker: JM Landsberg, TAMU

Title: A problem in graph theory and algebraic geometry

Abstract: The problem: let K_s,t denote the complete bipartite graph with s edges on the left and t on the right. What is the largest number of edges in an n vertex graph not containing K_s,t as a subgraph? The use of algebraic geometry: a suitable random subvariety on the Segre P^b\times P^b over F_q furnishes the vertex set and the zero set of a random polynomial on the Segre furnishes the edges. This is work of Boris Bukh. In his proof he has to avoid a bad set which has interesting geometry that I'll discuss.