[math-users] SISSA Geometry Seminars

[Ugo Bruzzo]

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SISSA GEOMETRY SEMINARS
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The following talks will be given on Friday, July 15th, in room 136
of SISSA Main Building. 

Prof. Andrei Caldararu (University of Wisconsin, Madison

Hochschild (co)homology for Azumaya orbifolds

h. 2:30 pm

Abstract: Tabuada and Van den Bergh have argued in a recent paper that Hochschild (co)homology of a smooth variety is not sensitive to the presence of a twisting by a Brauer class. I will argue that the situation is fundamentally different for orbifolds. Specifically, I will describe an HKR decomoposition of the Hochschild (co)homology of an orbifold endowed with a Brauer class, and I will explain how the invariants change when the Brauer class is turned on.  This gives mathematical justification for certain calculations in mirror symmetry of Vafa and Witten. (Joint work with Dima Arinkin.)

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Prof. Francesco Sala (University of Western Ontario, London, Canada)

From quivers to curves

h. 4 pm

Abstract.
Representation spaces of quivers play a preeminent role in geometric representation theory. For example, starting from them one can construct algebraic stacks whose K-theory has an associative algebra structure (K-theoretic Hall algebra), and smooth quasi-projective varieties (called Nakajima quiver varieties) whose K-theory provides a representation of these algebras.

In the first part of this talk, I will review the theory of Nakajima quiver varieties and K-theoretic Hall algebras associated with a quiver. Then I will explain what kind of new results one can obtain by replacing the representations spaces by the category of coherent sheaves over the complex projective line. (Joint work with O. Schiffmann.)
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