PIMS - SFU Discrete Math Seminar: Zeying Wang

Recently we proved a theorem for strongly regular graphs that provides numerical restrictions on the number of fixed vertices and the number of vertices mapped to adjacent vertices under an automorphism. We then used this result to develop some new techniques to study regular partial difference sets in abelian groups. We have proved several non-existence results and classification results of partial difference sets in abelian groups. Also we completely answered the question "For which odd positive integer $v>1$, can we find a Paley type partial difference set in an abelian group of order $v$?", a classical question from the 1990s. In this talk I plan to give an overview of these results.