I will discuss an idea of constructing a category associated with a pair of holomorphic Lagrangians in a hyperkähler 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 builds on earlier ideas of Haydys, Gaiotto-Moore-Witten, and Kapranov-Kontsevich-Soibelman.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
