Curvature, Koszul duality and Calabi–Yau structures

Abstract: I will talk about two aspects of Koszul duality. Firstly, Koszul duality for dg categories provides a way of modelling dg categories as certain curved coalgebras. This is a linearization of the correspondence of simplicial categories as simplicial sets (quasi-categories) and curved coalgebras have better formal properties than dg categories. Secondly, Koszul duality exchanges two self-dualities: smooth and proper Calabi–Yau structures. This is a generalization and conceptual explanation of the following phenomenon: For a topological space X with the homotopy type of a finite complex having an oriented Poincaré duality structure (with local coefficients) is equivalent to having a smooth Calabi–Yau structure on the dg algebra of chains on the based loop space of X. A similar phenomenon occurs for Lie algebras. This is joint work with Andrey Lazarev and with Manuel Rivera, respectively.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Comments: https://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09

Meeting ID: 918 7552 8987 Password: LAGOON

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).

Videos of the talks can be viewed here.

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