Tropical Fukaya Algebras

Explore the concept of Tropical Fukaya Algebras in this lecture by Sushmita Venugopalan, based on joint work with Chris Woodward. Delve into the effects of multiple cut operations on symplectic manifolds and the resulting collection of cut spaces with relative normal crossing divisors. Examine the impact of these cuts on curve count-based invariants, focusing on the Fukaya algebra of a Lagrangian submanifold in the complement of relative divisors. Discover how the ordinary Fukaya algebra in the unbroken manifold relates to a 'broken Fukaya algebra' that counts 'broken disks' associated with rigid tropical graphs. Learn about the further degeneration leading to a 'tropical Fukaya algebra' with structure maps summing products over tropical graph vertices. Gain insights into this advanced topic in symplectic geometry and algebraic topology during this hour-long presentation at the Institut Henri Poincaré.