Sung-Soo Byun (Seoul National University)

Title: Spectral moments and Harer-Zagier type recursion formulas in random matrix theory
Abstract: Random matrix theory enjoys an intimate connection with various branches of mathematics. One prominent illustration of this relationship is the Harer-Zagier formula for spectral moments, which serves as a well-known example demonstrating the combinatorial and topological significance inherent in random matrix statistics. While the Harer-Zagier formula originates from the study of the moduli space of curves, it also gives rise to a fundamental formula in the study of spectral moments of classical random matrices. In this talk, I will introduce Harer-Zagier type formulas for classical Hermitian Gaussian random matrix ensembles and present recent progress across various models.

Cheol-Hyun Cho (Seoul National University)

*TBA

Dogancan Karabas (Kavli IPMU) 

*TBA

Sin-Myung Lee (Korea Institute for Advanced Study)

Title: Deformed W-algebras and representations of quantum affine algebras, and their super analogues

Abstract: There are several instances where a vertex algebra and a quantum group, two different algebraic structures that evolved from simple finite-dimensional complex Lie algebras, are found out to be related in a deep way. This talk is about one such example, that is: a q-deformation of classical W-algebras and the Grothendieck ring of a module category of quantum affine algebras are isomorphic. After reviewing this connection, we discuss its super type A analogue which comes from a recent understanding of W-algebras in connection with 4D N=4 super Yang-Mills theory.

Chihiro Matsui (The University of Tokyo)

Title: Quantum thermalization and solvability

Abstract: Thermalization of quantum systems is a long-standing problem in statistical mechanics. These days, it is believed that thermalization is explained by the Eigenstate Thermalization Hypothesis (ETH), whose statement is that (almost) all energy eigenstates are undistinguished from thermal states by macroscopic variables. 

On the other hand, it has been found that some quantum systems weakly violate the statement of ETH, by allowing the existence of non-thermal energy eigenstates. Such exceptional systems often exhibit solvability or partial solvability. 

In this talk, I will show several examples of solvable or partially solvable models, together with the evidence that they indeed do not relax to the thermal state. This talk is based on Phys. Rev. B 109, 104307 (2024) and arXiv:2409.03208. 

Anderson Vera (Institute for Basic Science - Center for Geometry and Physics)

Title: The tree-like part of the Le-Murakami-Ohtsuki functor

Abstract: The Le-Murakami-Ohtsuki invariant is a powerful invariant of 3-manifolds (universal among quantum invariants and finite-type invariants), in particular, it dominates all the Reshetikhin-Turaev invariants. The LMO invariant takes values in a space of graphs called Jacobi diagrams or Feynman diagrams. Its definition uses the Kontsevich integral of links and several combinatorial operations at the level of Jacobi diagrams. This invariant was extended to a functor (LMO functor) from a category of cobordisms between bordered surfaces by Cheptea-Habiro-Massuyeau. In this talk we show that some of the tree diagrams appearing as values in the image of a particular kind of cobordisms of a surface S (mapping cylinders) under the LMO functor are related with algebraic invariants of the surface.

Masahito Yamazaki (The University of Tokyo)

Title: Vertex Operator Algebras as Chiralization of Quiver Varieties

Abstract: We discuss the ``chiralization'' of quiver varieties into vertex operator algebras (VOAs). Physically, quiver varieties arise as the Higgs branch of 3d N=4 quiver gauge theories, and when we topologically-twist the 3d theory, its boundary theory can be identified with the VOA. This work is based on arXiv:2312.13363 [hep-th] and work in progress, with Ioana Coman, Myungbo Shim, and Yehao Zhou.

Mengxue Yang (Kavli IPMU)

Title: Conformal limit on Cayley components

Abstract: In 2014, Gaiotto conjectured that there is a biholomorphism between Hitchin components and spaces of opers on a punctured sphere via a scaling limit called the $hbar$-conformal limit. On a compact Riemann surface of $g ge 2$, this biholomorphism has been proven in 2016. Motivated by the study of higher Teichm"uller spaces, we may view the Hitchin components as a part of a larger family of special components called Cayley components. I will talk about the Cayley components and propose their conformal limit to be the generalized notion of opers of Collier—Sanders.