Seminar on "Generalized Fourier transforms for D-modules and applications"

Spring term 2026

The aim of this seminar is to study certain transformations for D-modules on vector spaces, tori and abelian varieties and to understand how they are related and how they interact.

More details, and references can be found in this seminar program.

Some of the references used in the program are gathered here.

The seminar will run hybridly in Chemnitz (room 633) and remotely on Zoom (link will be send out separately). We meet on Thursdays 13:45-15:15. The precise schedule is below (subject to modifications). Recordings of the talks can be downloaded here.

Schedule

  1. The Fourier transform on vector spaces and on affine tori. (David Suero Casado), 23.04.2026, (Notes, Blackboard Notes (with Introduction by Constantin Podelski))
  2. Applications for affine tori: Hypergeometric D-modules (Maximilian Göbel), 30.04.2026
  3. Abelian varieties: Fourier-Mukai for D-modules (Christian Sevenheck), 21.05.2026
  4. Applications for abelian varieties I: The structure theorem (Henry Dakin), 28.05.2026
  5. Applications for abelian varieties II: Perverse coherent sheaves (Andreas Hohl), 04.06.2026
  6. Fourier transform for extensions of an abelian variety by a product of a torus and a vector space (Constantin Podelski), 11.06.2026
  7. A unifying framework: 1-motives. (Thomas Krämer), 18.06.2026

Organizers: Constantin Podelski, Thomas Krämer, Christian Sevenheck