SDS Statistics Seminar Series

Topic

Connections between Graphs and Matrix Spaces

Speaker

Yinan LI, Assistant Professor, School of Artificial Intelligence, Wuhan University

Host

Kun FANG, Assistant Professor, School of Data Science, CUHK-Shenzhen

Date

9 May (Friday), 2025

Time

02:30 PM- 03:15 PM, Beijing Time

Format

Hybrid

Venue

Room 203, Teaching Complex C Building

Zoom Link

https://cuhk-edu-cn.zoom.us/j/92595826472?pwd=AYZdbbxqveEuC4nkJt3wyDC0ZpfjGw.1

Meeting ID: 925 9582 6472, Password: 756481

Language

English

Abstract

Given a graph G, we introduce its graphical matrix space, which consists of matrices whose non-zero entries can only be at those positions corresponding to edges in G. We establish correspondences between graph-theoretic properties of G and linear-algebraic properties of its graphical matrix spaces, the former of which include matching, acyclicity, connectivity, expansion and isomorphism. We then utilize these correspondences to generalize classical results in commutative algebra, proving the inequivalence between Kazhdan property and dimension expansion, and estimating the probability of sampling matrix spaces with the trivial automorphism groups. 

Based on joint work with Markus Bläser, Youming Qiao, Alexander Rogovskyy, Avi Wigderson, Yuval Wigderson, and Chuanqi Zhang （ArXiv: 2206.04815, 2212.13154, 2503.07299).

Biography

Yinan Li is an assistant professor at the school of artificial intelligence, Wuhan University. He obtained his PhD from the University of Technology Sydney, under the supervision of Prof Runyao Duan and Prof Youming Qiao. Before coming to Wuhan, he worked at CWI, the Netherlands as a postdoctoral researcher and worked at Nagoya University, Japan as a designated assistant professor. His research focuses on quantum computing and its interdisciplinary study with mathematics, physics, and theoretical computer science.