In this talk wewill discuss maximal cliques in Paley graphs, generalized Paley graphs, andPeisert graphs. We will consider some constructions of maximal cliques andtheir geometric interpretation. We will also present some results oneigenfunctions in these graphs.

Leonid Shalaginovreceived the Specialist and Ph.D. degrees in mathematics from Chelyabisk StateUniversity, Russia, in 2008 and 2011, respectively. He is currently a Professorwith the Department of Mathematics, Chelyabinsk State University. His researchinterests mainly lie in algebraic graph theory.