Date/Time : 25 Aug 2025 14:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Adeel Khan, Academia Sinica

I will discuss a new type of pullback operation on perverse sheaves, which is defined for morphisms of complex algebraic stacks equipped with a certain extra structure, namely that of a so-called relative exact (-1)-shifted symplectic fibration. These perverse pullbacks are closely related to classical operations such as vanishing cycles functors and the Fourier-Sato transform. They also vastly generalize the theory of Donaldson-Thomas invariants of Calabi-Yau threefolds, and we will sketch how they lead to a proof of a conjecture of Joyce about their functoriality. Time permitting, I will attempt to briefly survey some applications of these constructions to topics like cohomological Hall algebras, curve counting on Landau-Ginzburg models, and the period sheaves for Hamiltonian G-spaces conjectured by Ben-Zvi, Sakellaridis, and Venkatesh. This is a report on joint work in progress with Tasuki Kinjo, Hyeonjun Park, and Pavel Safronov.

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