Perverse sheaves and relative Langlands duality


Wang, J. (2021). Perverse sheaves and relative Langlands duality. Perimeter Institute. https://pirsa.org/21090015


Wang, Jonathan. Perverse sheaves and relative Langlands duality. Perimeter Institute, Sep. 17, 2021, https://pirsa.org/21090015


          @misc{ pirsa_PIRSA:21090015,
            doi = {10.48660/21090015},
            url = {https://pirsa.org/21090015},
            author = {Wang, Jonathan},
            keywords = {Mathematical physics},
            language = {en},
            title = {Perverse sheaves and relative Langlands duality},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {sep},
            note = {PIRSA:21090015 see, \url{https://pirsa.org}}


The program of Ben-Zvi--Sakellaridis--Venkatesh connects the construction of L-functions in number theory with S-duality of boundary conditions in 4d. In particular this predicts certain equivalences of categories between equivariant D-modules on the formal loop space of a smooth variety X and equivariant quasi-coherent sheaves on a Hamiltonian manifold. I discuss an extension of this conjecture to certain singular varieties X and the possibility of quantizing the equivalence. I will explain joint work with Yiannis Sakellaridis on computing a certain factorization algebra which plays a role in the story. 

Zoom Link: https://pitp.zoom.us/j/95543248994?pwd=bmZIRnEyLzZnNmlEWW5oNTEwaEhNUT09