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Luis Ferroni:Valuative invariants for large classes of matroids

Time: Wed 2021-10-20 10.15 - 11.15

Location: Zoom meeting ID: 654 5562 3260

Participating: Luis Ferroni (Università di Bologna)

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Abstact: In this talk we will exhibit a systematic way of computing valuative invariants for the class of sparse paving and paving matroids. Such families are conjecturally predominant among all matroids. In particular, we obtain nice expressions for the volume, the Tutte polynomial, the Kazhdan-Lusztig polynomial, the Ehrhart polynomial, the gamma polynomial, the Derksen-Fink invariant and many other valuative invariants for all such matroids. As two remarkable consequences, we obtain examples of matroid polytopes that are not Ehrhart positive, we show that some large classes of matroids are Kazhdan-Lusztig non-degenerate and Kazhdan-Lusztig gamma-positive.

Zoom meeting ID: 654 5562 3260

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