Speaker: Sam Bardwell-Evans (Institute for Basic Science Center for Geometry and Physics)

Title: Global Kuranishi Charts for Moduli Spaces of Pseudoholomorphic Bordered Riemann Surfaces

Abstract: Moduli spaces of pseudoholomorphic curves and bordered Riemann surfaces with Lagrangian boundary conditions are fundamental objects in symplectic geometry, and especially in Lagrangian Floer theory. These spaces are in general highly singular and must be regularized in order to be useful. The Kuranishi structure method of Fukaya-Oh-Ohta-Ono provides such a regularization, but these structures are usually themselves highly complicated and difficult to work with. In the case of curves, Abouzaid-McLean-Smith and Hirschi-Swaminathan have recently constructed comparatively simple Kuranishi structures, known as global Kuranishi charts. We present an analogous result for moduli spaces of arbitrary pseudoholomorphic bordered Riemann surfaces. The techniques are closely related to those of FOOO and are analytic and differential-topological in nature.