Homological mirror symmetry and higher genus invariants: May 22-26, 2017

Organized By: Mohammed Abouzaid, Denis Auroux, Ron Donagi, Kenji Fukaya, Tony Pantev

Mirror symmetry’s most spectacular predictions are those about enumerative invariants of Calabi-Yau threefolds, which exhibit intricate structures when studied for all degrees and genera. This
workshop will focus on new developments whose goal is to provide a conceptual approach to the study of such invariants, and its main component will be 4 week-long lecture series:

Nicholas Sheridan: Counting curves using the Fukaya category
Kevin Costello and Si Li: The higher genus B-model
Tony Pantev: Non-commutative Hodge structures
John Pardon: Virtual fundamental cycles in Floer theory

An overall theme will be the use of categorical techniques to lift the idea of curve counting, which has a clear geometric origin in the setting of symplectic topology, to an abstract framework where it can be formulated in algebraic geometry as well, in such a way that the two sides of mirror symmetry can be directly compared. The lectures of Sheridan, Costello-Li, and Pantev will thus have, as unifying theme, the notion of using Hochschild (co)-homology and variants thereof as a receptacle for invariants of Gromov-Witten type.

The target audience for the workshop will be advanced graduate students, postdocs, and researchers in nearby subject areas.

Application deadline for this event has passed