- Series
- Combinatorics Seminar
- Time
- Friday, October 7, 2016 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- John Wilmes – Georgia Tech
- Organizer
- Esther Ezra
A graph is strongly regular'' (SRG) if it is k-regular, and every pair of adjacent (resp. nonadjacent) vertices has exactly λ (resp. μ) common neighbors. Paradoxically, the high degree of regularity in SRGs inhibits their symmetry. Although the line-graphs of the complete graph and complete bipartite graph give examples of SRGs with exp(Ω(√n)) automorphisms, where n is the number of vertices, all other SRGs have much fewer---the best bound is currently exp(˜O(n9/37)) (Chen--Sun--Teng, 2013), and Babai conjectures that in fact all primitive SRGs besides the two exceptional line-graph families have only quasipolynomially-many automorphisms. In joint work with Babai, Chen, Sun, and Teng, we make progress toward this conjecture by giving a quasipolynomial bound on the number of automorphisms for valencies k>n5/6. Our proof relies on bounds on the vertex expansion of SRGs to show that a polylogarithmic number of randomly chosen vertices form a base for the automorphism group with high probability.