北京雁栖湖应用数学研究院

白淑亮

姜子麟

2026年06月26日 16:00 至 17:00

A3-4-101

Zoom 204 323 0165 (BIMSA)

This talk concerns spectral properties of subcubic graphs and presents results from two recent papers, one joint with Hricha Acharya and Benjamin Jeter, and the other with Shenwei Huang. Both works address problems in spectral graph theory through a common approach: constructing linear-algebraic bridges that translate eigenvalue constraints into structural graph-theoretic conditions. In the first part of the talk, we study the median eigenvalues of connected subcubic graphs. We resolve questions raised by Fowler and Pisanski and by Mohar by showing that, with the sole exception of the Heawood graph, the median eigenvalues of any connected subcubic graph lie in the open interval (−1,1). In the second part, we turn to the classification of connected subcubic graphs with no eigenvalues in (−1,1), completing an investigation initiated by Guo and Royle. We determine all such graphs, showing that only two infinite families and finitely many sporadic examples occur. We conclude the talk by discussing several open problems suggested by these results and by the broader interplay between spectral and structural properties of subcubic graphs.

Zilin Jiang received his Bachelor’s degree in Mathematics from Peking University in 2011, and his Ph.D. in Algorithms, Combinatorics, and Optimization from Carnegie Mellon University in 2016. He subsequently worked as a postdoctoral researcher at the Technion – Israel Institute of Technology from 2016 to 2018, and then served as an Applied Mathematics faculty member (postdoctoral) at the Massachusetts Institute of Technology from 2018 to late 2020. He is currently a Full Professor at Arizona State University. His research interests include discrete geometry, extremal graph theory, and topological combinatorics.