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University of Sydney Algebra Seminar

Gaston Burrull (University of Sydney)

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

Top-heaviness and unimodality of Bruhat intervals

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.