Seeking the Smooth Schubert Varieties

Abstract: Schubert varieties in the flag variety G/B of a linear algebraic group G over an algebraically closed field were originally defined by Chevalley in his famous lost paper, where he also showed that the singular locus of a Schubert variety has codimension at least two. Perhaps unintentionally, he also remarked that Schubert varieties are probably smooth. This talk will give a survey of the global smoothness results for Schubert varieties in G/B. The results use a nice mixture of the combinatorics of the Weyl group of G and the geometry of G/B.

Refreshments will be served at 2:45 p.m. (Math Lounge, MATX 1115).