Quantum Topology and Field Theory Seminar
Yale University
Spring 2026
Yale University
Spring 2026
Organizers: Andrew Neitzke, Surya Raghavendran, Charlie Reid, Ka Ho Wong
Calendar:
Time: 4:30-5:30pm
Location: KT801
Abstract: Skein modules are algebraic objects that somehow "encode" links in a 3-dimensional manifold, in a way reminiscent of homology; they have many interesting connections to physics, representation theory, knot theory (via the Jones polynomial) and non-commutative algebra. In this talk I will give a broad introduction and overview of the topic and then discuss a new, elementary proof (due to myself and Renaud Detcherry) of finite dimensionality of the Kauffman bracket skein modules, originally done by Gunningham-Jordan-Safronov.
Time: 4:30-5:30pm
Location: KT801
Abstract: The"Schur index" is typically defined as a protected operator count in 4d N=2 superconformal field theories. It turns out in fact that one can define it for a generic 4d N=2 theory, conformal or not, by using the holomorphic-topological twist. Its categorification, namely the space of holomorphic-topological local operators, is expected to be a Poisson vertex algebra. However, for a general non-conformal theory, not much is known about the shape of this PVA. For 4d N=2 gauge theories with matter, I will formulate this PVA as a (relative) Lie algebra cohomology problem and then for the case of pure SU(2) Seiberg-Witten theory propose an explicit answer for the cohomology.
Time: 2:00-3:00pm
Location: KT801
Abstract: I will explain some results on the localization and deformation theory of vertex algebras, algebraic objects encoding a class of topological associative algebras generalizing the enveloping algebra of an affine Kac-Moody Lie algebra. I will also explain how these results can be used to give geometric constructions of free field realizations, embeddings of these algebras into infinite dimensional Weyl algebras, motivated by the physics of 4d N=2 superconformal field theories. All new results that will be presented are in joint work with Sujay Nair.
Time: 4:30-5:30pm
Location: KT801
Abstract: We give an algorithm to reduce the number of generators of the Khovanov chain complex of torus braids $(\sigma_1\sigma_2 \dots\sigma_{n−1})^k$ on $n$ strands. I will begin the talk with context on the stable Khovanov homology of torus links leading to the open question of the structure of their homology theory, as well as potential applications to open questions concerning the colored Jones polynomial. Next I will discuss our work, joint with Carmen Caprau, Nicolle Gonzalez, and Radmila Sazdanovic, using Bar-Natan Gaussian elimination, that gives our whittled complex $\mathcal{FT}_n^k$. The whittled complex is homotopy-equivalent to the original Khovanov chain complex but with a reduced number of generators. After sketching the proof, I will end the talk discussing related future projects.
Time: 4:30-5:30pm
Location: KT801
Abstract: For a Lagrangian submanifold in a CY3, Ekholm and Shende defined a wavefunction living in the HOMFLY-PT skein module of the Lagrangian, which encodes open Gromov-Witten invariants in all genus. In this talk, we study a skein-valued cluster theory that generalizes quantum cluster theory and allows us to compute these wavefunctions in a range of examples. Our results agree with the physical prediction known as the topological vertex. Along the way we introduce a skein dilogarithm and prove a pentagon relation, generalizing previously known forms of the pentagon identity. This talk is based on joint works with Schrader, Zaslow, and Shende.
Time: 4:30-5:30pm
Location: KT801
Abstract: TBA
Time: 4:30-5:30pm
Location: KT801
Abstract: I will describe a construction of a q-series invariant (BPS q-series, also known as the Z-hat invariant) associated to a 3-manifold decorated by an embedded link. These q-series depend only on the class of the link in the skein module, and hence define a homomorphism from the skein module to the space of q-series. The image of this homomorphism is conjectured to exhibit holomorphic quantum modularity, which suggests a new approach to Langlands duality for skein modules via q-series.
Time: 4:30-5:30pm
Location: KT801
Abstract: TBA
Time: 4:30-5:30pm
Location: KT801
Abstract: TBA
Time: 4:30-5:30pm
Location: KT801
Abstract: TBA
Time: 4:30-5:30pm
Location: KT801
Abstract: TBA
Time: 4:30-5:30pm
Location: KT801
Abstract: TBA
Time: TBA
Location: KT801
Abstract: TBA
Time: 4:30-5:30pm
Location: KT801
Abstract: TBA
Time: 4:30-5:30pm
Location: KT801
Abstract: TBA