An Application of Symplectic Topology to Algebraic Geometry

Explore a 42-minute lecture on the application of symplectic topology to algebraic geometry, delivered by Laurent Côté from Harvard University at the University of Miami. Delve into Rouquier's concept of dimension for triangulated categories and Orlov's conjecture regarding the bounded derived category of coherent sheaves. Discover how the speaker and collaborator Shaoyun Bai made progress on this conjecture using symplectic geometry methods and homological mirror symmetry. Gain insights into Weinstein manifolds, the Koshi property, and additive invariance as the lecture covers motivation, heuristic summaries, and quantitative symmetry. Engage with the potential for future research in this fascinating intersection of mathematical disciplines.