Constructible Sheaves and Filtered D-Modules

Explore a 50-minute lecture on Constructible Sheaves and Filtered D-modules presented by Bhargav Bhatt from the University of Michigan. Delve into the Riemann-Hilbert correspondence and its connection between constructible sheaves and D-modules on complex algebraic varieties. Examine the theory of mixed Hodge modules and the significance of the "Hodge" filtration in algebraic geometry applications. Discover how the Hodge filtration becomes automatic in the p-adic world, allowing for the functional attachment of filtered D-modules to constructible sheaves on algebraic varieties over p-adic fields. Learn about the potential applications of this functor, including its use in deriving Kollár's vanishing theorem for higher direct images of the canonical bundle from the BBDG decomposition theorem. This talk presents ongoing joint work with Jacob Lurie, offering insights into advanced topics in algebraic geometry and sheaf theory.