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Geometry Topology Dynamical Systems Seminar by Oliver Pechenik
Monday, Oct 16, 2017
4 p.m. - 5 p.m. Location: CB2 1.202

Oliver Pechenik

University of Michigan

Deformed cohomology of flag varieties

If we have three Hermitian matrices A+B=C, Horn's problem asks what we can say about the eigenvalues of C if given knowledge of the eigenvalues of the two summands. The surprising answer (as finally resolved resolved in the late `90s by work of Klyachko, Knutson and Tao) is a system of linear inequalities controlled by the classical Schubert calculus of Grassmannians. In 2006, Belkale and Kumar introduced a deformation of the cohomology of generalized flag varieties in order to describe solutions to more general such eigencone problems. They proved that their product was well-defined via geometric invariant theory. Another proof was supplied by Graham and Evens using relative Lie algebra cohomology. We give an essentially elementary proof, applicable to a more general family of products that we introduce. We also show how another specialization of this new product identifies intersections of Schubert varieties that behave nicely under projection maps. (Joint work with Dominic Searles.)

Contact Info:
Anh Tran, 972-883-6587
Questions? Email me.

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