MIT Symplectic Seminar

Building 2, 449

Speaker: Zihong Chen (MIT)Title: Quantum Steenrod operations and Fukaya categoriesAbstract: Fix a closed monotone symplectic manifold X. The cyclic open-closed map is a map from the cyclic homology of the Fukaya category to the S1 equivariant quantum cohomology of X. It is a key ingredient in the study of noncommutative Hodge theory on the A-side, and has various applications to enumerative mirror symmetry (e.g. Ganatra-Perutz Sheridan). Using this as a starting point, I will discuss my work in progress on categorifying characteristic p enumerative invariants. Via the cyclic open-closed map, we give a Fukaya-categorical interpretation of the quantum Steenriod operations due to Fukaya and Wilkins. I will discuss an application of this perspective by giving an arithmetic proof, involving quantum Steenrod operations, of the unramified exponential type conjecture first proved by Pomerleano-Seidel (23’) using completely different geometric considerations. The argument uses Katz’s classical theorem on local monodromy, and is a ’reduction mod p’ type argument in symplectic topology.