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

Mon, 21/05/201811:00-12:30
IIAS, Eilat hall, Feldman Building, Givat Ram
First speaker: Daniel kalmanovich, HU
Title: On the face numbers of cubical polytopes
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
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.