Academic Report of School of Mathematical Sciences [2026] No. 042

(Series Report for High-Level University Construction No. 1301)

Title：Natural graph spectra

Speaker：Ziqing Xiang, Professor (Southern University of Science and Technology)

Time：10:00-11:00, May. 13, 2026

Location：Huixing Building Room 501

Abstract： We call a graph matrix natural if it can be obtained from the adjacency matrix via a fixed sequence of linear combination, matrix multiplication and Hadamard multiplication. Typical examples of natural graph matrices are adjacency matrix, adjacency matrix of the complement graph, Laplacian matrix, distance matrix. In this talk, we demonstrate the existence of a natural graph matrix whose spectrum determines the structures of almost all graphs, which answers an open problem by van Dam and Haemers in 2003.

Speaker Profile：Ziqing Xiang is an associate professor in the Department of Mathematics at Southern University of Science and Technology and at the Shenzhen National Center for Applied Mathematics, as well as a National-Level Young Talent. He is the recipient of the 2022 Kirkman Medal from the International Society for Combinatorics and Its Applications. His research interests focus primarily on combinatorics and representation theory. In 2023, he proved that the only compact combinatorial designs of even strength are symmetric designs and Witt designs. In 2026, he constructed a natural graph spectrum capable of determining the structure of random graphs. His research findings have been published in journals such as Advances in Mathematics, Forum of Mathematics, and Sigma.

Faculty and students are welcome to attend!

Invited by: Zejun Huang

School of Mathematical Sciences

May 8, 2026