Algebraic Geometry Seminar
Duality for abelian gauge theories via derived geometry
2026/03/12 (Thu.) 10:00~11:00
- Date : 2026/03/12 (Thu.) 10:00~11:00
- Location : Seminar Room 617, Institute of Mathematics (NTU Campus)
-
Speaker : Owen Gwilliam (University of Massachusetts Amherst)
- Organizer : Ionut Ciocan-Fontanine and Adeel Khan and Y.P. Lee (AS)
- Abstract :
The theory of electromagnetism --- also known as Yang-Mills theory for the group U(1) --- admits a systematic generalization involving connections on higher U(1)-bundles. We will articulate these theories using sheaves and derived stacks, offering a synthesis of differential (or Deligne) cohomology and the BV formalism. This framework allows us to formulate in easy terms the physical idea of electromagnetic, or abelian, duality: such abelian theories on n-dimensional manifolds come in pairs, swapping gauge theory for p-bundles with gauge theory for (n-p-2)-bundles. Given time, we may discuss how these methods apply to the 6d self-dual 2-form gauge theory that appears as part of the 6d N=(1,0) and (2,0) superconformal theories, which are supposed to be the origins of the geometric Langlands correspondence . This is joint work in progress with Chris Elliott, Ingmar Saberi, and Brian Williams.
