As the underlying configuration behind many elegant finite structures, partial difference sets have been intensively studied in design theory, finite geometry, coding theory, and graph theory. Over the past three decades, there have been numerous constructions of partial difference sets in abelian groups with high exponent, accompanied by numerous very different and delicate techniques. Surprisingly, we manage to unify and extend a great many previous constructions in a common framework, using only elementary methods. The key insight is that, instead of focusing on one single partial difference set, we consider a packing of partial difference sets, namely, a collection of disjoint partial difference sets in a finite abelian group. This conceptual shift leads to a recursive lifting construction of packings in abelian groups with increasing exponent.

This is joint work with Jonathan Jedwab.

Bio: Shuxing Li received his Ph.D. degree in Mathematics from Zhejiang University, China, in 2016. He was an Alexander-von-Humboldt Postdoctoral Fellow from October 2017 to September 2019, at Otto von Guericke University Magdeburg, Germany. Since November 2019, he has been a PIMS Postdoctoral Fellow at the Department of Mathematics, Simon Fraser University. His research focuses on finite configurations with beautiful symmetry, which involves algebraic and combinatorial design theory, algebraic coding theory, finite geometry and discrete geometry. He received the 2018 Kirkman Medal from the Institute of Combinatorics and its Applications.