IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

Shuo Zhang (Morningside Center of Mathematics): Composed Dehn twist exact sequence through quilts and $(A_\infty,n)$ modules

We prove the quilted Floer cochain complexes form $(A_\infty,n)$ modules over the Fukaya category $Fuk(M \times M^-)$. Then we prove that when we restrict the input to mapping cones of product Lagrangians and graphs, the resulting bar-type complex can be identified with bar complex from ordinary Floer theory. As an application we prove two long exact sequences conjectured by Seidel that relates the Lagrangian Floer cohomology of a collection of (possibly intersecting) Lagrangian spheres $L_i$ and the fixed point Floer cohomology of composed Dehn twists $\tau_{L_1} o ...  \tau_{L_n}$ along them.

Kifung Chan (Chinese University of Hong Kong): Mirror symmetry of nonabelian group actions

This talk is based on joint work with Naichung Conan Leung. We study the mirror symmetry of nonabelian group actions on symplectic manifolds. We show that the presence of a nonabelian symmetry imposes constraints on non-displaceable Lagrangian branes. This work is motivated by our earlier proposal to understand 3d mirror symmetry via $SYZ$-type transforms.

May Sela (The Hebrew University of Jerusalem): Mirror symmetry for open Gromov–Witten invariants of Fano manifolds

In this talk, I will introduce a class of numerical invariants associated with matrix factorizations, constructed to mirror open Gromov–Witten invariants. Matrix factorizations are algebraic objects expected to correspond, under mirror symmetry, to Lagrangian submanifolds in Fano manifolds. I will describe the non-Archimedean framework required for defining these invariants and present results concerning their structure. This is joint work with J. Solomon.