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.