Algebra and Lie Theory Seminar
Mondays at 14:15
Research I, Room 111
The Algebra and Lie Theory Seminar is a graduate research
seminar.
This semester we will concentrate on the structure of diagonal
Lie algebras and on the FernandoKac subalgebras of generalized
Harish Chandra modules.
Special Event: Minicourse on Geometry of Grassmannians
Evgeny Smirnov (Universität Bonn), Research I Seminar Room
Monday, March 9, 13:45 
Grassmannians. Schubert varieties. Cohomology ring
of a Grassmannian. Poincaré duality. Pieri formula.
LittlewoodRichardson rule (w/o proof). Applications to enumerative
problems. 
Tuesday, March 10, 15:15 
Singularities of Schubert varieties: BottSamelson resolutions.
Zelevinsky's small resolutions. 
Wednesday, March 11, 17:00 
Plücker embedding. Plücker relations. Standard monomials.
Plücker relations generate the homogeneous ideal of a Grassmannian.
Desription of the singular loci of Schubert varieties. 
Special Event: Minicourse on Geometry of Flag Varieties
Valentina Kiritchenko (Jacobs University), Research I Seminar Room
Monday, April 27, 13:45 
Varieties of complete flags. Main example:
complete flags in a 3space. Picard group of a flag variety and
irreducible representations of semisimple groups. Borel
presentation for the cohomology ring of a flag variety. 
Monday, May 4, 13:45 
Bruhat cell decomposition, Bruhat order, Schubert cycles.
Schubert cycles in the Borel presentation, divided difference
operators, Schubert polynomials. 
Monday, May 11, 13:45 
Schubert calculus, ChevalleyPieri formula for the product of a
Schubert cycle with a divisor. BottSamelson resolutions of
Schubert cycles in a flag variety. 
