Speaker: Spencer Backman, HU

Title: Cone valuations, Gram's relation, and flag-angles

Abstract: Interior angle vectors of polytopes are semi-discrete analogues of f-vectors that take into account the interior angles at faces measured by spherical volumes. In this context, Gram's relation takes the place of the Euler-Poincaré relation as the unique linear relation among the entries of the interior angle vectors. Simple normalized cone valuations naturally generalize spherical volumes, and in this talk I will show that Gram's relation is the unique linear relation for angle vectors associated to a cone valuation. Our proof goes by way of establishing a connection with the combinatorics of zonotopes. I will then introduce flag-angle vectors as a counterpart to flag-f-vectors of polytopes, and determine their linear relations by coalgebra methods and a connection to the flag-vectors of lattices of flats. This is joint work with Sebastian Manecke and Raman Sanyal.

Title: Cone valuations, Gram's relation, and flag-angles

Abstract: Interior angle vectors of polytopes are semi-discrete analogues of f-vectors that take into account the interior angles at faces measured by spherical volumes. In this context, Gram's relation takes the place of the Euler-Poincaré relation as the unique linear relation among the entries of the interior angle vectors. Simple normalized cone valuations naturally generalize spherical volumes, and in this talk I will show that Gram's relation is the unique linear relation for angle vectors associated to a cone valuation. Our proof goes by way of establishing a connection with the combinatorics of zonotopes. I will then introduce flag-angle vectors as a counterpart to flag-f-vectors of polytopes, and determine their linear relations by coalgebra methods and a connection to the flag-vectors of lattices of flats. This is joint work with Sebastian Manecke and Raman Sanyal.

## Date:

Mon, 22/10/2018 - 11:00 to 13:00

## Location:

Rothberg CS building, room B500, Safra campus, Givat Ram