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Holomorphic Floer Theory and the Fueter Equation

[HYBRID WORKSHOP] New Four-Dimensional Gauge Theories October 24, 2022 - October 28, 2022

October 25, 2022 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Aleksander Doan (University of Cambridge; University College London)
Location: MSRI: Simons Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

Holomorphic Floer Theory And The Fueter Equation


I will discuss an idea of constructing a category associated with a pair of holomorphic Lagrangians in a hyperkahler manifold, or, more generally, a manifold equipped with a triple of almost complex structures I,J,K satisfying the quaternionic relation IJ =-JI= K. This category can be seen as an infinite-dimensional version of the Fukaya-Seidel category associated with a Lefschetz fibration. While many analytic aspects of this proposal remain unexplored, I will argue that in the case of the cotangent bundle of a Lefschetz fibration, our construction recovers the Fukaya-Seidel category. This talk is based on joint work with Semon Rezchikov and has many connections to recent work of Bousseau.

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Holomorphic Floer Theory And The Fueter Equation

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