Monodromy and derived equivalences


Okounkov, A. (2022). Monodromy and derived equivalences. Perimeter Institute. https://pirsa.org/22060008


Okounkov, Andrei. Monodromy and derived equivalences. Perimeter Institute, Jun. 06, 2022, https://pirsa.org/22060008


          @misc{ pirsa_PIRSA:22060008,
            doi = {10.48660/22060008},
            url = {https://pirsa.org/22060008},
            author = {Okounkov, Andrei},
            keywords = {Mathematical physics},
            language = {en},
            title = {Monodromy and derived equivalences},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {jun},
            note = {PIRSA:22060008 see, \url{https://pirsa.org}}

Andrei Okounkov Columbia University


This will be an introductory discussion of our joint work with Roman Bezrukavnikov. Given a symplectic resolution X, one may study its Gromov-Witten theory and the monodromy group of the curve-counting functions in the K\"ahler variables. There is also a large group of derived autoequivalences of X coming from its quantization in large prime characteristic, as studied by Bezrukavnikov and collaborators. Conjecturally, the action of the latter group on K(X) is identified with the former group, and we prove this for many $X$.