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K-State Today

February 18, 2016

Mathematics Colloquium lecture Feb. 18

By Reta McDermott

Rina Anno, Massachusetts Institute of Technology, will present "Categorical Actions and Flag Varieties" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Thursday, Feb. 18, in 122 Cardwell Hall.

The abstract for the lecture is derived categories of coherent sheaves on cotangent bundles to complex varieties such as flag varieties, partial flag varieties, and Grassmannians sometimes admit categorical actions by structures such as braid groups, affine braid groups, the algebra sl(2), nil affine Hecke algebras, or the category of tangles. In some cases, these actions are understood on both sides of homological mirror symmetry, for example, spherical twists on the B-side corresponding to Dehn twists on the A-side. We are going to review several examples of such actions and their underlying mechanics, and propose an action of the category of so-called "generalized braids" between all varieties of partial flags in C^n, that incorporates what is possibly the best known example of such categorical action, the Khovanov-Thomas braid group action on the full flag variety.