Speaker:  Tan Nhat Tran, Binghamton University
Title: Algebraic Combinatorics Meets Probability Theory: Vines and MAT-Labeled Graphs
Time: 2:30 PM, Monday, March 10, 2025
Place:  Malott 206

Abstract: This talk explores the connection between two concepts from distinct areas of mathematics. The first concept, a vine, is a graphical model used to represent dependent random variables. Initially introduced by Joe (1994) and later formalized by Cooke (1997), vines have become an active research area with applications in probability theory and uncertainty analysis. The second concept, MAT-freeness, is a combinatorial property in the theory of freeness of the logarithmic derivation module of hyperplane arrangements. First studied by Abe-Barakat-Cuntz-Hoge-Terao (2016) and further developed by Cuntz-Muecksch (2020), MAT-freeness has been a topic of increasing interest. In particular, for graphic arrangements, Tsujie and I recently demonstrated that MAT-freeness is completely characterized by the existence of certain edge-labeled graphs, known as MAT-labeled graphs. I will show that there is a fascinating equivalence between the categories of locally regular vines and MAT-labeled graphs. Notably, this leads to an equivalence between the categories of regular vines and MAT-labeled complete graphs. This work is joint with H.M. Tran (Hanoi) and S. Tsujie (Hokkaido).


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