Some pseudorandom graphs

Abstract: A classical construction associates to any Sidon set a graph without $4$-cycles. We investigate some properties of these graphs in the case of the Sidon sets constructed by Forey, Fres\' an and myself using methods of algebraic geometry. In particular, this provides deterministic families of Ramanujan graphs with semi-circle and other interesting explicit asymptotic eigenvalue distributions. Based on joint work with A. Forey and J. Fres\' an and discussions with Y. Wigderson and T. Schramm.

Mathematics

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2025)