Seminar on geometry, symmetry, and physics, Fall 2021

(aka mirror symmetry/related topics)

Usually Tuesdays 1:00-2:00pm on Zoom

Organized by Lev Borisov, Emanuel Diaconescu, and Chris Woodward

Tuesday, November 16, 2021, 1pm on Zoom

Title: Family Floer mirror and mirror symmetry for rank 2 cluster varieties

The Gross-Hacking-Keel mirror is constructed in terms of scattering diagrams and theta functions. The ground of the construction is that scattering diagrams inherit the algebro-geometric analogue of the holomorphic disks counting. With Yu-shen Lin, we made use this idea and gave first non-trivial examples of family Floer mirror. Then with Sam Bardwell-Evans, Hansol Hong, and Yu-shen LIn, we construct a special Lagrangian fibration on the non-toric blowups of toric surfaces that contains nodal fibres, and prove that the fibres bounding Maslov 0 discs reproduce the scattering diagrams. As a consequence, we can then illustrate the mirror duality between the A and X cluster varieties.

Email organizer for zoom link

Counting pointlike instantons virtually without gluing

Guangbo Xu, Texas A&M

Location: Email organizers for zoom info

Date & time: Tuesday, 07 December 2021 at 1:00PM - 2:00PM

Abstract: In defining symplectic invariants such as Gromov-Witten invariants or Floer homology, a crucial step is the construction of the virtual fundamental cycle or the virtual fundamental chain (VFC). In this highly involved procedure, one typically needs the so-called "gluing construction" to obtain local charts. It was Tian who firstly noticed that to construct VFC in situations such as Gromov-Witten invariants, one does not necessarily need gluing. In this talk, I will review the VFC construction in Gromov-Witten theory and briefly explain Tian's idea. Then I will show how to apply this idea to define virtual counts of pointlike instantons in gauged linear sigma model. This talk is based on the joint work with Tian.