Olivetti Club

Fiona YoungCornell University
Where polytope geometry meets probability

Tuesday, April 26, 2022 - 4:35pm
Malott 532

Suppose we have a real-valued function defined on the set of subsets of a finite ground set E. What is the expected value of this function on a randomly chosen subset of E?

The story begins with the equivalence between generalized permutohedra and polymatroids, the latter being an example of the type of function described above. Any generalized permutohedron can be expressed as a signed Minkowski sum of simplices, and the summands control the signed beta invariants of the associated polymatroid and its contractions. It turns out that the signed Minkowski sum of simplices is intimately related to the expected rank polynomial of the polymatroid. Finally, we apply our results more generally to the type of functions described at the beginning.

Refreshments will be served in the lounge at 4:00 PM.