# Holomorphic Floer Theory and the Fueter Equation

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

**Speaker(s):**Aleksander Doan (University of Cambridge; University College London)

**Location:**SLMath: Eisenbud 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.

#### Holomorphic Floer Theory And The Fueter Equation

Please report video problems to itsupport@slmath.org.

**See more of our Streaming videos on our main
VMath Videos page.**