Seminars & Colloquia Calendar

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Frobenius Splitting Methods in Geometry and Representation Theory

Shrawan  Kumar, the John R. and Louise S. Parker distinguished professor of mathematics at the University of North Carol

Location:  Hill Center Room 705
Date & time: Wednesday, 26 October 2022 at 3:30PM - 4:30PM

Abstract: The theory of Frobenius Splitting has made a significant impact in the study of geometry and representation theory. The aim of the colloquium is to recall the basic definitions and results in the theory and how they are applied to solve some of the classical problems in geometry of flag varieties and representation theory of semisimple groups and their Kac-Moody analogs.Some of the applications include:

(1) Any Schubert variety X_w is normal, and has rational singularities (in particular, is Cohen-Macaulay).
(2) The linear system on X_w given by any regular weight embeds X_w as a projectively normal and projectively Cohen-Macaulay variety.

(3) The higher cohomology vanishing of dominant line bundles on Schubert Varieties.
(4) Demazure character formula.

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