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Luis Ferroni:Many valuations for many matroids

Time: Wed 2022-10-12 15.15 - 16.15

Location: 3721

Participating: Luis Ferroni (KTH)

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Abstract: Invariants are pervasive in matroid theory. Examples of invariants are the Tutte polynomial of the matroid, the f-vector of its Bergman Complex, the Ehrhart polynomial of its base polytope, or the Hilbert series of its Chow ring. In this talk I want to address two facts:
1) Why all of the above invariants (and many more!) are valuative under matroid polytope subdivisions.
2) How one can use the preceding fact to actually provide a fast way for computing arbitrary valuative invariants for a huge class of matroids called "split matroids".
In particular, I will show how one can use this general framework to attack conjectures on matroid theory in both ways: either to prove a conjecture for this large class of matroids (and hence, support it in general) or to build a counterexample. As applications one can build counterexamples to the Ehrhart positivity conjecture of De Loera et al., or support other conjectures in Kazhdan-Lusztig theory by Proudfoot et al.
This is joint work with Benjamin Schröter.