Aim: Developing Floer theory techniques for selected types of
generalized complex manifolds

Generalized complex geometry unifies complex and symplectic geometry, two important research areas in modern pure mathematics. While generalized complex (GC) structures in full generality are not yet well-understood, a number of important results from complex or symplectic geometry have already been extended to these more general structures. Further, complex and symplectic geometry are intimately related to each other via mirror symmetry, a conjectured duality between certain complex and symplectic manifolds discovered in theoretical physics in the context of string theory. This duality has been proven in special cases.

This project proposes an approach to extend homological mirror symmetry to certain subclasses and examples of GC manifolds, centred around three objectives:

(O1) Quantify the effect of stable GC compactifications of Landau-Ginzburg mirrors of del Pezzo surfaces on their Fukaya category.

(O2) Construct a Wrapped Fukaya category for oriented surfaces with log symplectic structures.

(O3) Develop and study a notion of 'holomorphic families of Fukaya categories'.

New to generalized (complex) geometry and want to know more? Visit the blog! 

Not a mathematician, but interested in what I do? Read the general introduction to FuSeGC or watch me speak at Soapbox Science Brussels 2021.