Mathematical Physics

The ground state of a bipartite quantum system resembles a thermal state from the perspective of an observer with access to only one of the two regions. This observation has led to the introduction of the entanglement Hamiltonian, which has numerous applications in quantum information and the study…

Non-abelian Hodge theory is a profound three-way equivalence between topological, smooth and holomorphic objects, i.e. representations of the fundamental group, flat connections and Higgs bundles. It is natural to explore a group-theoretic or multiplicative version — an enterprise that has been…

In this talk, I will present a sewing-factorization theorem for conformal blocks in arbitrary genus associated to a (possibly nonrational) $C_2$-cofinite VOA $V$. This result gives a higher genus analog of Huang-Lepowsky-Zhang's tensor product theory. Moreover, I will explain the relation between…

Inspired by recent work calculating the top weight cohomology of the moduli space $\mathcal{A}_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$, I will discuss a connection between matroids and compactifications of $\mathcal{A}_g$ that is anlogous to the…

I will give a gentle introduction to the moduli space of graphs and its fine moduli space cousin known as Outer Space. This moduli space of graphs has many applications to various branches of mathematical physics, algebraic geometry, and geometric group theory. It is a natural object to consider…

After an introduction to the notion of Leonard pairs, I explain their different uses. Then, I provide the definition of the associated Heun operator and how it allows us to simplify the computation of the quantum entanglement entropy. Finally, I show, in the simplest example, how the Bethe ansatz…

I will give a gentle introduction to the moduli space of graphs and its fine moduli space cousin known as Outer Space. This moduli space of graphs has many applications to various branches of mathematical physics, algebraic geometry, and geometric group theory. It is a natural object to consider…

In this talk, I will present the construction of the Yangian of a cotangent Lie algebra from the geometry of the equivariant affine Grassmannian. Furthermore, I will discuss how this quantum group can be dynamically twisted to a quantum groupoid over a neighborhood in the moduli space of G-bundles…

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…