Topological Fukaya categories, knots, and topological strings (C01)

• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 506632645

We plan to develop the theory of topological Fukaya categories into a powerful instrument. Topological Fukaya categories of special classes of spaces, such as symmetric products of Riemann surfaces, will serve as guides to advance the general perspective of categorified homological algebra. Such categories, with coefficient data in the form of perverse schobers will serve as a basis for the construction of categorified link invariants in low-dimensional topology. Such Fukaya categories will also be used to exhibit the spaces of BPS states as backbones for the integrable structures in topological string theory.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1624: Higher structures, moduli spaces and integrability
• Applicant Institution: Universität Hamburg
• Project Heads: Professor Dr. Tobias Dyckerhoff; Professor Dr. Jörg Teschner; Professor Dr. Paul Wedrich