SGGTC this Friday: Chris Woodward
Oleg Lazarev
Dear all,
This Friday Chris Woodward from Rutgers will give a talk at 1:00 in Math 417. We will meet at 11:30 in the lobby before his talk and go out for lunch.
Best, Oleg
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Chris Woodward: Tropical Fukaya algebras
Abstract: In many cases, the hardest part of computing Lagrangian Floer cohomology is to show that a particular Lagrangian is weakly unobstructed. For example, weak unobstructedness of fibers of SYZ fibrations are covered in several recent works. I will introduce a new tool, joint with Sushmita Venugopalan (Chennai) called the tropical Fukaya algebra, which is homotopy equivalent to the original Fukaya algebra and whose structure coefficients are counts of tropical graphs. The construction is similar to that of Eleny Ionel and Brett Parker, but we use a further Fulton-Sturmfels-type degeneration of the diagonal to remove all matching conditions. A corollary is that any tropical toric moment fiber is weakly unobstructed, where a tropical toric moment fiber is a fiber of a normal-crossing toric degeneration whose limit is contained in a toric component.
Abstract: In many cases, the hardest part of computing Lagrangian Floer cohomology is to show that a particular Lagrangian is weakly unobstructed. For example, weak unobstructedness of fibers of SYZ fibrations are covered in several recent works. I will introduce a new tool, joint with Sushmita Venugopalan (Chennai) called the tropical Fukaya algebra, which is homotopy equivalent to the original Fukaya algebra and whose structure coefficients are counts of tropical graphs. The construction is similar to that of Eleny Ionel and Brett Parker, but we use a further Fulton-Sturmfels-type degeneration of the diagonal to remove all matching conditions. A corollary is that any tropical toric moment fiber is weakly unobstructed, where a tropical toric moment fiber is a fiber of a normal-crossing toric degeneration whose limit is contained in a toric component.