The Pushforward Theorem and Applications

Explore a comprehensive lecture on the Pushforward Theorem and its applications, delivered by Tony Pantev from the University of Pennsylvania. Delve into the concept of relative shifted symplectic structures along the stalks of constructible sheaves of derived stacks on stratified spaces. Learn about a general pushforward theorem that produces relative shifted symplectic forms and discover techniques for computing these forms. Examine a universal construction of Poisson structures on derived moduli of Stokes data on smooth varieties, and understand how symplectic leaves arise from fixing irregular types and local formal monodromies at infinity. Follow the lecture's structure, covering topics such as the problem statement, recap, examples, honorable dice, nearby cycles, forms, and the pushforward process.