Prospects for Spectral Mirror Symmetry
Explore the cutting-edge research on spectral mirror symmetry in this advanced mathematics lecture. Delve into the construction of Fukaya categories from moduli spaces of discs and the potential for extending these concepts using higher-dimensional moduli spaces. Examine the challenges of curvature and anomaly resolution in non-exact symplectic manifolds, and discover how spectral rings can be utilized to lift current constructions beyond discrete rings. Learn about collaborative efforts to formulate this generalization, incorporate Lagrangian Floer theory into the new framework, and develop Floer-theoretic constructions yielding mirror varieties. Gain insights into the latest developments in symplectic geometry and its intersections with algebraic geometry and topology from Stanford University researcher Mohammed Abouzaid.