# Combinatorics: Daniel Kalmanovich and Or Raz (HU) "2 talks back-to-back"

First speaker: Daniel kalmanovich, HU Title: On the face numbers of cubical polytopes Abstract: Understanding the possible face numbers of polytopes, and of subfamilies of interest, is a fundamental question. The celebrated g-theorem, conjectured by McMullen in 1971 and proved by Stanley (necessity) and by Billera and Lee (sufficiency) in 1980-81, characterizes the f-vectors of simplicial polytopes. We consider f-vectors of cubical polytopes (these are polytopes in which each proper face is combinatorially a cube), where no such characterization is known, and investigate the following question: What is the minimal closed cone containing all f-vectors of cubical d-polytopes? We construct cubical polytopes showing that this cone, expressed in the cubical g-vector coordinates, contains the nonnegative g-orthant, thus verifying one direction of the Cubical Generalized Lower Bound Conjecture of Babson, Billera and Chan from 1997. Our polytopes also show that a natural cubical analogue of the simplicial Generalized Lower Bound Theorem does not hold. Based on joint work with Ron Adin and Eran Nevo.---------- Second speaker: Or Raz, HU Title: Symplectic geometric lattices are shellable Abstract: Geometric lattices were extensively studied, in part because they correspond to finite matroids. I define a symplectic geometric lattice in a set theoretic way similar to their classical counterparts, proving a few properties, for which the main one is a characterization of these lattices by atom orderings of which being shellable is a corollary of. In the same way that all geometric lattices are attained as sub-lattices of the the face lattice of the simplex, we have our lattices be sub-lattices of the face lattice of the Cross polytop. This makes them a natural candidate for the lattice of flats for symplectic matroids. ----------

## Date:

Mon, 21/05/2018 - 11:00 to 12:30

## Location:

IIAS, Eilat hall, Feldman Building, Givat Ram