Algebraic Combinatorics Seminar - Jonathan Jedwab

Title: Packings of partial difference sets

Abstract:

Partial difference sets are highly structured group subsets that occur in various guises throughout design theory, finite geometry, coding theory, and graph theory. They admit only two possible nontrivial character sums and so are often studied using character theory. The central question is to determine which groups contain a partial difference set with two specified nontrivial character sums. We consider an apparently more difficult question: which groups contain a large disjoint collection of such partial difference sets? This leads us to identify a certain subgroup as containing important structural information about the packing. With this insight, we are able to formulate a recursive construction of packings in abelian groups of increasing exponent. This allows us to unify and extend numerous previous results about partial difference sets using a common framework.

This is joint work with Shuxing Li, a 2019-2021 PIMS Postdoctoral Fellow.