Discrete mathematics

Speaker: 
Andy Hsiao
Speaker Affiliation: 
UBC

November 19, 2024

ESB 4133 (PIMS library)
Vancouver, BC
Canada

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Abstract: 

Matroids are combinatorial objects that abstract the notion of independence. Given any matroid, Feichtner and Yuzvinsky defined a graded commutative ring called the Chow ring, inspired by algebraic geometry. To each matroid, we can define a linear map called the mixed volume of the matroid, which completely determines the Chow ring. In a recent work by Braden, Huh, Matherne, Proudfoot, and Wang, they provide a decomposition of the Chow ring by decomposing the matroid using the deletion operation. Following a similar method, we give an inductive formula for computing the mixed volume of a matroid. This is joint work with Kalle Karu and Jonathan Yang.

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