Speaker
Hyeonjun Park
(KIAS)
Description
Modern enumerative invariants, such as Gromov--Witten invariants and
Donaldson--Thomas invariants, are defined through the virtual classes.
In this talk, I will introduce Lagrangian classes, whose existence was
conjectured by Joyce, as a generalization of the virtual classes via shifted
symplectic geometry. As applications, I will explain the construction of
(1) cohomological Hall algebras for 3-Calabi--Yau categories;
(2) cohomological field theories for gauged linear sigma models;
(3) relative Donaldson--Thomas theory for 4-dimensional log Calabi--Yau pairs;
(4) algebraic Fukaya categories for hyperkahler varieties. This is joint
work in progress with Adeel Khan, Tasuki Kinjo, and Pavel Safronov.