Mathematical Physics

This talk is based on my recent joint works arXiv:2405.18625, arXiv:2307.03831 with Joaquin Liniado and Florian Girelli. Based on Lie 2-groups, I will introduce a 3d topological-holomorphic integrable field theory W, which can be understood as a higher-dimensional version of the Wess-Zumino-Witten…

The correspondence of AGT sets up, in part, a connection between six-dimensional superconformal theories and 2d CFT. We will give a mathematical construction of 2d CFT from 6d SCFT which involves recent progress in our understanding of the holomorphic twist 6d superconformal symmetry. We then turn…

The underlying holomorphic structure of a generalized Kahler manifold has been recently understood to be a square in the double category of holomorphic symplectic groupoids (or (1,1)-shifted symplectic stacks). I will explain what this means and how it allows us to describe the generalized Kahler…

I'll discuss the representation theory of line operators in 3d holomorphic-topological theories, following recent work with Wenjun Niu and Victor Py. Examples of the line operators we have in mind include half-BPS lines in 3d N=2 supersymmetric theories (reinterpreted in a holomorphic twist). We…

Higgs branches in theories with 8 supercharges change as one tunes the gauge coupling to critical values. This talk will focus on six dimensional (0,1) supersymmetric theories in studying the different phenomena associated with such a change. Based on a Type IIA brane system, involving NS5 branes…

Deligne's category $D_t$ is a formal way to define the category of finite-dimensional representations of the group $GL_n$ with $n=t$ being a formal parameter (which can be specialized to any complex number). I will show how to interpolate the construction of the higher Hamiltonians of the Gaudin…

We will discuss some aspects of my recent preprint, joint with Victor Ginzburg, on Kostant-Whittaker reduction, a (deformation) quantization of restriction to a Kostant slice. We will explain how this functor can be used to prove conjectures of Ben-Zvi and Gunningham on parabolic induction, as well…

Skein theory forms a once-categorified 3d TQFT and assigns skein algebras to surfaces and skein modules to 3-manifolds. Motivated by physics, these modules are expected to satisfy a certain holonomicity property, generalizing Witten's finiteness conjecture of skein modules. In this talk, we will…

Chern-Simons theory is a topological quantum field theory which leads to link invariants, such as the Jones polynomial, through the expectation values of Wilson loops. The same link invariants also appear in a mathematical construction of Reshetikhin and Turaev which uses a trace on Yang-Baxter…

The operator algebraic approach to quantum field theory is called algebraic quantum field theory. In this setting, we consider a family of operator algebras generated by observables in spacetime regions. This has been particularly successful in 2-dimensional conformal field theory. We present roles…

I will review some recent progress in derived differential geometry, in particular pertaining to moduli stacks of solutions of elliptic partial differential equations on manifolds (with boundaries, and also with `logarithmic' boundaries, which include, for instance, manifolds with asymptotically…

In this talk, I will discuss how M2-M5 intersections in a twisted M-theory background yield the R-matrices of the quantum toroidal algebra of gl(1). These R-matrices are identified with the Miura operators for the q-deformed W- and Y-algebras. Additionally, I will show how the M2-M5 intersection (or…