Jul 2 – 7, 2018
IHES
Europe/Paris timezone

Deformations of Calabi-Yau categories and Poisson brackets of functions

Jul 6, 2018, 2:00 PM
1h
Marilyn and James Simons Conference Center (IHES)

Marilyn and James Simons Conference Center

IHES

35, route de Chartres 91440 Bures-sur-Yvette (France)

Speaker

Chris Brav

Description

We explicate two deformation problems for a smooth Calabi-Yau category C, showing in particular that the complexes underlying the Lie algebras controlling these deformation problems are shifts of negative cyclic and of cylic chains of C. Using these results, we show that the natural map from cyclic chains of C to functions on the `moduli of objects’ M_C is a map of (shifted) Lie algebras with respect to the deformation-theoretic Lie structure on cyclic chains and the Poisson bracket on functions induced by the Calabi-Yau structure on C. Our results give a chain level generalisations of classical constructions of Goldman for moduli of local systems and of Hitchin for GL(n)-Higgs bundles. This is joint work with Nick Rozenblyum.

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