Sunday, January 25, 2026
Ungar Bldg, Room 411
1:00pm
Dr. Umut Varolgunes, Koç University: Seidel’s quantum D-module through the choice of a
prequantization circle bundle
The usual Gysin exact sequence for a principal circle bundle can be interpreted as follows. First, consider the (tautological) long exact sequence of multiplication with the equivariant parameter in circle equivariant cochains upstairs. Then, prove that circle equivariant cochains upstairs is quasi-isomorphic to cochains downstairs, and finally that, up to chain homotopy, multiplication with equivariant parameter is the same as multiplication with a representative of the Euler class. In joint work with Ma-Mak Pomerleano, we use this viewpoint to prove that Seidel’s QDM on loop equivariant Hamiltonian Floer cochains (of an arbitrary non-degenerate Hamiltonian h), which depends on the choice of a cycle whose class is Poincare dual to the symplectic class, can be recovered from doing geometric circle action and loop rotation action equivariant Floer theory for functions hr+g(r) in the symplectization of a prequantization circle bundle whose Euler class is Seidel’s integral lift. This has potential applications to closed string mirror symmetry, which I will touch upon in my talk.
2:00pm
Dr. Enrique Becerra, CINVESTAV: The Stringy Spectrum from Formal Loop Spaces
We introduce the stringy spectrum of a smooth projective complex variety as an intrinsic index-theoretic invariant defined on its formal loop space. The construction is based on an equivariant Dolbeault-type index with respect to loop rotation by roots of unity and produces a finite Puiseux polynomial encoding a refined spectrum of rational weights. A canonical projection of the spectrum recovers the holomorphic Euler characteristic, providing a refined Euler invariant. The stringy spectrum admits two complementary interpretations: as the holomorphic sector of a Dirac index on the formal loop space, and as a global analogue of the Steenbrink spectrum arising from a Lefschetz pencil, in close analogy with Morse theory. The construction extends naturally to orbifolds and smooth Deligne–Mumford stacks, incorporates twisted sectors and Chen–Ruan phenomena, and satisfies a refined McKay correspondence.
3:00pm
Dr. Daniel Pomerleano, University of Massachusetts: Frobenius intertwiners and the p-adic Gamma class
In recent joint work with Bai and Seidel, we formulated a conjecture regarding the existence of an overconvergent Frobenius structure on the quantum cohomology of Fano manifolds. This candidate structure is constructed from Morita’s p-adic Gamma function, and its conjectural overconvergence is intrinsically linked to integrality properties of Givental’s fundamental solution. In this talk, I will describe progress toward reinterpreting classical Dwork-type constructions within the framework of symplectic topology. If time permits, I will extend these considerations to the Calabi-Yau case.
IMSA activities are generously supported through grant funding from the Simons Foundation, National Sciences Foundation and the University of Miami.
