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UID:c070544369b4dc95d1cd32bb494437ef
CATEGORIES:Colloquia
CREATED:20221024T161413
SUMMARY:Frobenius Splitting Methods in Geometry and Representation Theory
LOCATION:Hill Center Room 705
DESCRIPTION:Abstract: The theory of Frobenius Splitting has made a significant impact i
 n the study of geometry and representation theory. The aim of the colloquiu
 m 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 va
 rieties and representation theory of semisimple groups and their Kac-Moody 
 analogs.Some of the applications include:\n(1) Any Schubert variety X_w is 
 normal, and has rational singularities (in particular, is Cohen-Macaulay).\
 n (2) The linear system on X_w given by any regular weight embeds X_w as a 
 projectively normal and projectively Cohen-Macaulay variety.\n \n (3) The h
 igher cohomology vanishing of dominant line bundles on Schubert Varieties.\
 n (4) Demazure character formula.\n
X-ALT-DESC;FMTTYPE=text/html:<p><span style="font-family: inherit; font-size: 1rem; caret-color: auto;">
 Abstract: The theory of Frobenius Splitting has made a significant impact i
 n the study of geometry and representation theory. The aim of the colloquiu
 m 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 va
 rieties and representation theory of semisimple groups and their Kac-Moody 
 analogs.Some of the applications include:</span></p><p>(1) Any Schubert var
 iety X_w is normal, and has rational singularities (in particular, is Cohen
 -Macaulay).<br /> (2) The linear system on X_w given by any regular weight 
 embeds X_w as a projectively normal and projectively Cohen-Macaulay variety
 .<br /> <br /> (3) The higher cohomology vanishing of dominant line bundles
  on Schubert Varieties.<br /> (4) Demazure character formula.</p>
CONTACT:Shrawan  Kumar, the John R. and Louise S. Parker distinguished professor of mathematics at the University of North Carol
DTSTAMP:20260828T185344
DTSTART;TZID=America/New_York:20221026T153000
DTEND;TZID=America/New_York:20221026T163000
SEQUENCE:0
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