Speaker: Hyeonjun Park (KISA)
Time: Jun 12 14:00:00
Location: R1210, SIMIS
In this talk, I will explain the construction of Lagrangian classes for perverse sheaves in cohomological Donaldson-Thomas theory, whose existence was conjectured by Joyce. The two key ingredients are a relative version of the DT perverse sheaves and a hyperbolic version of the dimensional reduction theorem. As a special case, we recover Borisov-Joyce/Oh-Thomas virtual classes in DT4 theory. As applications, I will explain how to construct the following structures from the Lagrangian classes: (1) cohomological Hall algebras for 3-Calabi-Yau categories, (2) relative Donaldson-Thomas invariants for Fano 4-folds with anti-canonical divisors, (3) refined surface counting invariants for Calabi-Yau 4-folds, (4) cohomological field theories for gauged linear sigma models. This is joint work in progress with Adeel Khan, Tasuki Kinjo, and Pavel Safronov.
About Speaker:
Hyeonjun Park is a June E Huh Fellow (KIAS Assistant Professor, Postdoc) at Korea Institute for Advanced Study. He got his PhD at Seoul National University under the supervision of Professor Young-Hoon Kiem. Research interests: Virtual fundamental cycles Intersection theory of algebraic stacks Shifted symplectic structures Donaldson-Thomas theory of Calabi-Yau 4-folds Cohomological Donaldson-Thomas theory
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