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Hodge structures through Topological Quantum Field Theory

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If you have a question about this talk, please contact Nils Prigge.

Topological Quantum Field Theories are powerful categorical tools that provide deep insight into the behaviour of topological invariants under gluing. In this talk, we will review some properties of TQFT , including duality and classification problems, as well as their lax counterparts and how to construct them.

Using this procedure, we will construct a lax monoidal TQFT that computes the mixed Hodge structure on the cohomology of representation varieties. For that, Saito’s mixed Hodge modules will play an important role as quantizations of Hodge structures.

Joint work with M. Logares and V. Muñoz.

This talk is part of the Junior Geometry Seminar series.

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