Quantum Steenrod operations of symplectic resolutions


Lee, J.H. (2023). Quantum Steenrod operations of symplectic resolutions. Perimeter Institute. https://pirsa.org/23100091


Lee, Jae Hee. Quantum Steenrod operations of symplectic resolutions. Perimeter Institute, Oct. 12, 2023, https://pirsa.org/23100091


          @misc{ pirsa_PIRSA:23100091,
            doi = {10.48660/23100091},
            url = {https://pirsa.org/23100091},
            author = {Lee, Jae Hee},
            keywords = {Mathematical physics},
            language = {en},
            title = {Quantum Steenrod operations of symplectic resolutions},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {oct},
            note = {PIRSA:23100091 see, \url{https://pirsa.org}}

Jae Hee Massachusetts Institute of Technology (MIT)


We study the quantum connection in positive characteristic for conical symplectic resolutions. We conjecture the equivalence of the p-curvature of such connections with (equivariant generalizations of) quantum Steenrod operations of Fukaya and Wilkins, which are endomorphisms of mod p quantum cohomology deforming the Steenrod operations. The conjecture is verified in a wide range of examples, including the Springer resolution, thereby providing a geometric interpretation of the p-curvature and a full computation of quantum Steenrod operations. The key ingredients are a new compatibility relation between the quantum Steenrod operations and the shift operators, and structural results for the mod p quantum connection recently obtained by Etingof--Varchenko.


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