Schubert combinatorics and geometry

Wednesday, May 9, 2007 - 11:15am - 12:15pm
Lind 409
Alexander Yong (University of Illinois at Urbana-Champaign)
The topic of Schubert varieties of homogeneous spaces G/P is at the interface between algebraic geometry and combinatorics. I'll describe work on two themes.

The first is Schubert calculus: counting points in intersections of Schubert varieties. A goal has been combinatorial rules for these computations. I'll explain the carton rule which manifests basic symmetries of the numbers for the Grassmannian case; this version also has the advantage of generalizing to (co)minuscule G/P.

The second concerns singularities of Schubert varieties. I'll give a combinatorial framework for understanding invariant of singularities via a notion we call interval pattern avoidance.

The first half of this talk is joint work with Hugh Thomas (U. New Brunswick) while the second half is joint work with Alexander Woo (UC Davis).