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The Fukaya category of a log symplectic surface

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Charlotte Kirchhoff-Lukat
MIT, Cambridge (USA) and KU Leuven (Belgium)
Die, 21/11/2023 - 13:30 - 14:30
MPIM Lecture Hall

Log symplectic structures constitute an important class of Poisson structures with well-behaved degeneracies: Since they are symplectic almost everywhere, many powerful techniques from symplectic geometry apply, but the degeneracy loci introduce local invariants.

As a first step in the effort to extend Floer theory, Fukaya categories and mirror symmetry to Poisson structures with degeneracies, I will present the construction of Floer cohomology and a Fukaya category for log symplectic structures on oriented surfaces, with a focus on the additional features of the theory arising from the degeneracy locus, and how this theory detects and is modified by the degeneracy loci of the structure.


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