Seminar Event Detail

Algebraic Geometry

Date:  Wednesday, February 07, 2018
Location:  4096 East Hall (4:10 PM to 5:30 PM)

Title:  Finiteness in quantum K-theory of flag varieties

Abstract:   A quantum product on the K-theory of a variety was defined by Givental, deforming the usual tensor product just as quantum cohomology deforms the cup product. In contrast to cohomology, it is far from obvious that the product is finite in the deformation parameters: from the definition, contributions from curves of arbitrarily high degree appear. For Grassmannians - or more generally, cominuscule homogeneous varieties - Buch, Chaput, Mihalcea, and Perrin showed the product is finite, by carrying out a detailed study of the Kontsevich space of stable maps.

I will describe work with Linda Chen and Hsian-Hua Tseng in which we show that the quantum K-theory is finite for all flag varieties G/B of simply laced type. Our methods are rather different, taking advantage of properties of the K-theoretic J-function.


Speaker:  David Anderson
Institution:  Ohio-State University

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