The 40th Anniversary of Shenzhen University and the 40th Anniversary of Mathematics Department

Liyuan scholar Colloquium forty-four

Lecture Title: Erds-Ko-Rado Type Theorems for Permutation Groups

Speaker：Prof. Xiang Qing (Southern University of Science and Technology)

Lecture time：October 17, 2023 16:30-17:30 p.m.

Lecture location: 514 Huixing Building, Yuehai Campus, Shenzhen University, China

Overview：

The Erds-Ko-Rado (EKR) theorem is a classical result in extremal set theory. It states that when k < n/2, any family of k-subsets of [n] := {1,2,...,n}, with the property that any two subsets in the family have nonempty intersection, has size at most；equality holds if and only if the family consists of all k-subsets of [n] containing a fixed element.

Here we consider EKR type problems for permutation groups. In par- ticular, we focus on the action of the 2-dimensional projective special linear group PSL(2,q) on the projective line PG(1,q) over the finite fieldwhere q is an odd prime power. A subset S of PSL(2,q) is said to be an intersecting family if for any g1,g2 ∈ S, there exists an element x ∈ PG(1,q) such that xg1 = xg2 . It is known that the maximum size of an intersecting family in P SL(2, q) is q(q − 1)/2. We prove that all intersecting families of maximum size must be cosets of point stabilizers for all odd prime powers q > 3. This talk is based on joint work with Ling Long, Rafael Plaza, and Peter Sin.

Speaker Introduction：

Qing Xiang is the Chair Professor and Head of the Department of Mathematics at Southern University of Science and Technology (SUSTech). Prof. Qing Xiang received his PhD degree from Ohio State University in 1995. His research interests include combinatorial design, finite geometry, coding theory and additive combinations. He has published 99 papers in the top international journals of combinatorial mathematics, such as J. Combin. He has published 99 papers in international journals. He has been in charge of more than 10 research projects, including the U.S. National Natural Science Foundation of China (NSFC) and the Overseas Research Fund for Overseas Scholars (ORF) of the National Natural Science Foundation of China (NNSFC). He is currently presiding over one key project of the National Natural Science Foundation of China and one project of Overseas Senior Research Fellowship. He has made more than 60 presentations and invited lectures at international conferences.

Teachers and students are welcome to participate!

School of Mathematical Sciences

October 15, 2023