Six operations in differential geometry

Abstract: Recently, there has been a lot of interest in abstract six-functor formalisms: machines that take as input geometric spaces of some kind and output (higher) categories, usually some version of sheaves. This assignment should be appropriately local, and comes with an intricate system of functorialities and coherences. Six-functor formalisms have been constructed in algebraic and analytic geometry, leading to powerful categorical invariants. I will discuss a new six-functor formalism in differential geometry, which roughly takes a manifold to the derived ∞-category of bornological modules for its sheaf of smooth functions, and give some applications to the smooth representation theory of Lie groups and Lie groupoids, to TQFTs and to geometric PDEs.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Comments: The Zoom link is

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 has a strong focus on Representation Theory and Algebraic Geometry and their many interactions covering topics such as homological mirror symmetry, stability conditions, derived categories, dg-categories, Hochschild cohomology, moduli spaces and algebraic stacks, derived algebraic geometry and other topics.

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.

Video recordings of past talks until April 2022 can still be viewed on the ICMS webpage here.

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