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K-State Today

February 7, 2013

Mathematics Colloquium today

Submitted by Reta McDermott

Gabriel Kerr from University of Miami will present "Polynomials, Quivers and Derived Categories" at 2:30 p.m. Thursday, Feb. 7, in 122 Cardwell Hall.

Abstract: There is a rich history in representation theory relating polynomial singularities to quivers. The McKay correspondence illustrates an instance of this relationship, generalizing classical observations in invariant theory. A modern version of this correspondence involves an equivalence between several derived categories, some of which result from a mirror symmetry interpretation.

In this talk Kerr will detail the most basic example of this correspondence. He will explain how to define a moduli space that parameterizes the mirror models in this case. Thinking of this moduli as a space of stability conditions, he will recover classical structures from representation theory. He will conclude with an explanation of how these results give new insights into derived Morita theory and algebraic geometry.

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