UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 07, 2017

939 Evans Hall

3:45PM: Double ramification cycles and tautological relations

Emily Clader

Tautological relations are certain equations in the Chow ring of the moduli space of curves. I will discuss a family of such relations, first conjectured by A. Pixton, that arises by studying moduli spaces of ramified covers of the projective line. These relations can be used to recover a number of well-known facts about the moduli space of curves, as well as to generate very special equations known as topological recursion relations. This is joint work with various subsets of S. Grushevsky, F. Janda, X. Wang, and D. Zakharov.

5:00PM: Hodge Theory on Matroids

Chris Eur

We discuss recent developments by June Huh and others on the application of Hodge techniques to matroids. We introduce the Chow ring of a matroid and explore its relationship to the usual Chow rings in toric geometry. We then discuss its role in the solution of the two major conjectures concerning the unimodality of the Whitney numbers---the Rota-Welsh Conjecture and the Dowling-Wilson Conjecture.

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