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.
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