UBC Math Department Colloquium: Chi Hoi (Kyle) Yip

Given a prime power q≡1(mod4), the Paley graph of order q is the graph defined over 𝔽q (the finite field with q elements), such that two vertices are adjacent if and only if their difference is a square in 𝔽q. A clique in the Paley graph over 𝔽q is a subset of 𝔽q that induces a complete subgraph, equivalently, a subset of 𝔽q such that all pairwise differences are squares in 𝔽q.

In this talk, I will report some new results related to cliques in Paley graphs, Paley-like graphs, and their generalizations. I will also discuss some interesting connections between Paley graphs and number theory. Joint work with Shamil Asgarli, Andries E. Brouwer, Sergey Goryainov, Seoyoung Kim, Greg Martin, Leonid Shalaginov, and Semin Yoo.