Title: p-adic Hodge Theory and Combinatorics.
Speaker: Som Phene, University of Michigan.
Time: Tuesday, 26 July, 4:30 pm.
Venue: ***Ramanujan Hall***
Abstract: We introduce combinatorial geometries and geometric lattices. We show an equivalence between them followed by the correspondence of their finite versions with simple matroids. We then introduce the characteristic polynomial of a matroid, the Mobius algebra of a lattice. We hope to shed light on the result of log concavity for simple matroids (Huh 2012 for matroids representable in char 0, Huh-Katz 2012 for each representable matroid, Adiprasito-Huh-Katz 2018 for general matroids).