Description
Title: A tale of two Fourier transforms: universal Jacobians and hyper-Kähler varieties
Abstract: Fourier transforms for abelian varieties have been studied for decades since the work of Beauville in the 80s. The purpose of this talk is to explain how these ideas can be applied to the study of two different types of geometric objects: universal compactified Jacobians and hyper-Kähler varieties. For universal compactified Jacobians, Fourier transforms lead to the construction of the intrinsic cohomology ring; for hyper-Kähler varieties of K3[n]-type, Fourier transforms lead to a proof of the multiplicative Orlov conjecture for homological motives. I will explain the proofs in both settings, which rely on completely different geometric ingredients but are parallel in a certain sense. Further open questions will be discussed if time permits. This talk is based on joint work with Younghan Bae, Davesh Maulik, and Qizheng Yin.
Best,
Junliang