- 3/15/2023: 3-manifolds and modular tensor categories

- 9/13/2021: On the Vafa-Witten theory on closed four-manifolds

### March 15, 2023

TITLE: 3-manifolds and modular tensor categories

ABSTRACT: I will report on some progress in understanding a novel correspondence between modular tensor categories (MTC) and 3-manifolds. In particular, it has been conjectured that to any Seifert manifold M3 with three singular fibres, one can canonically associate a MTC, which is expected to describe the infrared of T[M3], a 3d QFT obtained from wrapping M5 branes over special Lagrangians inside CY3. We examine the conjecture by studying the generalised symmetries and the SymTFT from compactifying topological sectors of M theory using the framework of differential cohomology. We generalise the conjecture to more general Seifert manifolds with arbitrary number of singular fibres. I will also comment on some interesting connections to G2 manifolds. The talk is based on our work in progress with Federico Bonetti and Sakura Schafer-Nameki.

### September 13, 2021

TITLE: Kondo line defect and affine oper/Gaudin correspondence

ABSTRACT: It is well-known that the spectral data of the Gaudin model associated to a finite semisimple Lie algebra is encoded by the differential data of certain flat connections associated to the Langlands dual Lie algebra on the projective line with regular singularities, known as oper/Gaudin correspondence. Recently, some progress has been made in understanding the correspondence associated with affine Lie algebras.

I will present a physical perspective from Kondo line defects, physically describing a local impurity chirally coupled to the bulk conformal field theory. The Kondo line defects exhibit interesting integrability properties and wall-crossing behaviors, which are encoded by the generalized monodromy data of affine opers. In the trigonometric setting, this reproduces the known ODE/IM correspondence in the physics literature. I will explain how the recently proposed 4d Chern Simons theory provides a new perspective which suggests the possibility of a physicists’ proof. Along the way, I will also present new examples of ODE/IM correspondences. The talk is based on [2003.06694][2010.07325][2106.07792] in collaboration with D. Gaiotto, J Lee, B. Vicedo.