Date: Friday, April 10, 2015
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Rootsystem combinatorics and Schubert calculus
Abstract: We discuss some results in Schubert calculus obtained using the combinatorial model of roottheoretic Young diagrams (RYDs). In joint work with A. Yong, we give nonnegative rules for the Schubert calculus of the (co)adjoint varieties of classical type, and use these rules to suggest a connection between planarity of the root poset and polytopality of the nonzero Schubert structure constants. In joint work with O. Pechenik, we introduce a deformation of the cohomology of generalized flag varieties. A special case is the BelkaleKumar deformation, introduced in 2006 by P. BelkaleS. Kumar. This construction yields a new, short proof that the BelkaleKumar product is welldefined. Another special case preserves the Schubert structure constants corresponding to triples of Schubert varieties that behave nicely under projections. We also present an RYD rule for the BelkaleKumar product for flag varieties of type A (after the puzzle rule of A. KnutsonK. Purbhoo).
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Speaker: Dominic Searles
Institution: U. Illinois
Event Organizer: Sergey Fomin
