A Fourier Transform for Abelian Fibrations

Explore a lecture on the theory of Fourier transform for abelian fibrations with singular fibers. Delve into the extension of the Beauville decomposition for abelian schemes and its governance of the perverse filtration. Examine applications confirming the motivic decomposition conjecture of Corti-Hanamura and the multiplicativity of the perverse filtration. Investigate the interaction between the perverse filtration and tautological classes. Learn about the potential construction of a Lefschetz decomposition compatible with the Fourier transform in the Lagrangian setting. Gain insights into this complementary work to Davesh Maulik's talk, based on joint research with Davesh Maulik and Qizheng Yin.