Abstract:
I will explain the construction of a Fourier-Mukai transform in the setting of Lurie's spectral algebraic geometry, and discuss its fundamental properties. This can be regarded as a derived enhancement of the classical Fourier-Mukai transform for abelian varieties.
As an application, this yields a common refinement of three facets of the phenomenon known as "level–rank duality": (1) positive-energy representations of LU(n)_k and LSU(k)_n (representation theory), (2) the level-rank duality on equivariant TMF (homotopy theory), and (3) the "strange duality" of Verlinde bundles (algebraic geometry). This is joint work in progress with Daniel Berwick-Evans and Akira Tominaga.
- Organizer: Centre for Quantum Mathematics
- Address: Campusvej 55, 5230 Odense M
- Contact Email: qm@sdu.dk
- Add to your calendar: https://eom.sdu.dk:443/events/ical/016074e9-bfe7-4f24-984f-e86d0b9da472