Department of Mathematics Colloquium


Abstract 

Let p
be a prime number congruent to 1 modulo 4 and let F_{p}
be a finite field with p
elements. The Paley graph with p
vertices is defined as the graph having the vertex set F_{p},
where two vertices are adjacent if and only if their difference is a
square of in F_{p}. In this talk, I will discuss the problem of counting the number of complete subgraphs in the Paley graph. The goal of this talk is to show that determining the number of such subgraphs can be reduced to counting the number of points on a certain variety (i.e., a geometric object defined by a system of polynomial equations) over F_{p}. _{} 