SMS scnews item created by Kevin Coulembier at Wed 20 Apr 2022 0837
Type: Seminar
Distribution: World
Expiry: 1 Jun 2022
Calendar1: 29 Apr 2022 1200-1300
CalLoc1: Carslaw 273
CalTitle1: Algebra Seminar, Burrull: Top-heaviness and unimodality of Bruhat intervals
Auth: kevinc@p717i.pc (assumed)

# Algebra Seminar: Burrull -- Top-heaviness and unimodality of Bruhat intervals

Gaston Burrull (University of Sydney)

Friday 29 April, 12-1pm, Place: Carslaw 273

Title: Top-heaviness and unimodality of Bruhat intervals

Abstract: I will introduce the sequences b^w_i of Betti numbers associated with Schubert
varieties.  These sequences are always top-heavy, but not always unimodal.  In the case
of dominant elements in the affine Weyl group, the behavior of the corresponding
sequences b^w_i is very much described by a convex polyhedron that only depends on a
dominant weight and the Cartan matrix of the corresponding (finite) root system.  I will
measure how top-heavy these sequences are, and state some results and conjectures.  I
will show plenty of pictures and examples in ranks 2 and 3.