广州数学大讲坛第五期

第四十六讲—中南大学Nhat Tran Tan教授学术报告

题目：A Common Combinatorial Framework for Graphs, Vines, and Single-Peaked Domains

时间：2026年10月23日上午10:00—12:00

地点：理学实验楼312室

报告人：Nhat Tran Tan 教授

摘要：Many combinatorial structures arising in different areas of mathematics exhibit striking similarities, suggesting the existence of a common underlying principle. In this talk, I will present a framework that unifies several seemingly unrelated objects, including MAT-labeled graphs from the theory of hyperplane arrangements, regular vines from probability theory, and maximal Arrow’s single-peaked domains from social choice theory. The key idea is an axiomatic recursive construction based on two simple operations, called splitting and merging, which completely characterizes all of these objects. This viewpoint leads to explicit correspondences between them and provides new combinatorial and axiomatic characterizations of maximal single-peaked domains.

The talk requires only elementary linear algebra and basic combinatorics, and no background in hyperplane arrangements, probability, or social choice theory will be assumed. If time permits, I will also explain how the same framework naturally extends to extremal lattices from formal concept analysis and extremal binary matrices with no triangles from combinatorial matrix theory. The talk is based on recent joint work with H. M. Tran (Phenikaa) and S. Tsujie (Hokkaido).

报告人简介：

Nhat Tran Tan is a Professor in the School of Mathematics and Statistics at Central South University in Hunan, China. He received his Ph.D. from Hokkaido University in 2020 under the supervision of Masahiko Yoshinaga. He subsequently held a JSPS Postdoctoral Fellowship at Hokkaido University, an Alexander von Humboldt Research Fellowship at Ruhr University Bochum, a postdoctoral position at Leibniz University Hannover, and a Robert Riley Visiting Assistant Professorship at SUNY Binghamton University. His research interests lie in algebraic combinatorics and discrete mathematics, particularly hyperplane arrangements, root systems, posets, and graphs, as well as their connections to probability theory and social choice theory. His work has appeared in journals including Forum Math. Sigma, Ann. Sc. Norm. Super. Pisa Cl. Sci., Int. Math. Res. Not. IMRN, J. Lond. Math. Soc., J. Combin. Theory Ser. A, Algebr. Comb., European J. Combin., and Adv. Appl. Math.