2026-09-20T10:23:42Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1554172024-06-28T04:06:07Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Seidel, Paul
Lee, Jae Hee
Massachusetts Institute of Technology. Department of Mathematics
2024-06-27T19:51:59Z
2024-06-27T19:51:59Z
2024-05
2024-05-15T16:20:35.961Z
https://hdl.handle.net/1721.1/155417
https://orcid.org/0000-0002-7022-8735
In this thesis, we apply techniques from symplectic Gromov--Witten theory to study the equivariant quantum connections in positive characteristic. The main examples of interest arise from symplectic resolutions. We introduce equivariant generalizations of the quantum Steenrod operations of Fukaya, provide nontrivial computations in the example of the cotangent bundle of the projective line, and explore the relationship with Varchenko's construction of mod p solutions to the quantum differential equation. We then prove the compatibility of the equivariant quantum Steenrod operations with the quantum differential and difference connections. As a consequence, we obtain an identification of our operations for divisor classes with the p-curvature of the quantum connection in a wide range of examples.
Ph.D.
Massachusetts Institute of Technology
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
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https://creativecommons.org/licenses/by-nc-nd/4.0/
Equivariant quantum connections in positive characteristic
Thesis
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Doctoral
Doctor of Philosophy
Publication
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<Abstract>In this thesis, we apply techniques from symplectic Gromov--Witten theory to study the equivariant quantum connections in positive characteristic. The main examples of interest arise from symplectic resolutions. We introduce equivariant generalizations of the quantum Steenrod operations of Fukaya, provide nontrivial computations in the example of the cotangent bundle of the projective line, and explore the relationship with Varchenko's construction of mod p solutions to the quantum differential equation. We then prove the compatibility of the equivariant quantum Steenrod operations with the quantum differential and difference connections. As a consequence, we obtain an identification of our operations for divisor classes with the p-curvature of the quantum connection in a wide range of examples.</Abstract>
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