Lie Group/Quantum Mathematics Seminar

Time Friday, 12:10 pm to 1:10 pm (Eastern time).

Place Hill 705 or online via Zoom (see below for the Zoom link and passcode).

YouTube channel Rutgers Lie Groups Quantum Math Seminar.

Starting from Spring, 2008, the Lie Group Seminar and Quantum Mathematics Seminar have merged together to a single seminar called the Lie Group/Quantum Mathematics Seminar. The information on seminar talks can also be found in the Seminars & Colloquia Calendar page in the department. For the Lie Group/Quantum Mathematics seminar in previous semesters, see this page. For talks in the Quantum Mathematics Seminar from Spring, 1998 to Fall, 2007, see this page. For a few years before 2008, the Quantum Mathematics Seminar shared the time and place with the Algebra Seminar. For talks in both the Algebra and Quantum Mathematics Seminars in these few semesters, see the page for the Previous Rutgers Algebra Seminars. For all the seminars and colloquia in the department, see the Seminars & Colloquia Calendar page.

Fall, 2026

In this semester, the seminar will be mostly in person. Occasionally there might be online talks using zoom. See the information below on each talk. For online talks, here is the information for the zoom meeting:

Zoom link: https://rutgers.zoom.us/j/93921465287

Meeting ID: 939 2146 5287

Passcode: 196884, the dimension of the weight 2 homogeneous subspace of the moonshine module

Some of the talks will be recorded and will be placed in the YouTube Channel for the seminar.

Upcoming talk

• Speaker Qixuan Fang, Rutgers University at Newark
  • Title Meromorphic open-string vertex algebras, modules and a Dirac-like operator on spin manifolds
  • Time/place 10/16/2026, Friday, 12:10 noon (Easten time), Hill 705 (in person)
    
  • Abstract In this talk, we discuss a construction of a sheaf of boson-fermion meromorphic open-string vertex algebras and a sheaf of their canonically twisted modules from spinor bundles on a spin manifold. In particular, we realize the Dirac operator as a component of some special vertex operator when acting on ground spinors. This is joint work with Yi-Zhi Huang and Fei Qi. If time permits, we will discuss generalization of this construction to Courant algebroids, which includes the special case of realizing the (three-form twisted) de Rham differential as a vertex operator component on differential forms.

Upcoming related talk

• Speaker Yi-Zhi Huang, Rutgers University
  • Title Mathematical construction and study of conformal-field-theoretic tensor categories
  • Event Mathematical Physics Seminar
  • Time/place 10/15/2026, Thursday, 12:10 pm (Easten time), Hill 705 (in person)
    
  • Abstract Tensor categories now play an important role in the study of the representation theory of infinite-dimensional Lie algebras and other algebras related to two-dimensional conformal field theories. They have also been viewed as a type of generalized symmetries in physics (symmetry topological field theories) and are used to describe and study fractional quantum Hall systems, anyons, and other phenomena in condensed matter physics. Recently there are a lot of progresses in the general construction and study of tensor categories arising from the mathematical approaches to conformal field theories, especially in the representation theory of vertex operator algebras. I will discuss some of these main progresses and will also discuss the connection with the probability construction of the Liouville conformal field theory.

All scheduled talks

• Speaker Yi-Zhi Huang, Rutgers University
  • Title Boson-fermion meromorphic open-string vertex algebras, twisted modules , and a Dirac -like operator on a spin manifold
  • Time/place 9/18/2026, Friday, 12:10 pm (Easten time), Hill 705 (in person)
    
  • Abstract Meromorphic open-string vertex algebras are noncommutative generalizations of lower-bounded vertex algebras. It was introduced in 2012 in order to generalize the Heisenberg and lattice vertex operator alghebras to curved Riemannian manifolds. This talk is on a joint work with Qixuan Fang and Fei Qi giving a construction of boson-fermion meromorphic open-string vertex algebras, their canonically twisted modules and a Dirac-like operator from a spin manifold.
  • Archive paper arXiv:2607.05817 (contianing only the construction of boson-fermion meromorphic open-string vertex algebras and their canonically twisted modules; the second paper is still in preparation).

• Speaker Milen Yakimov, Northeastern University
  • Title Reflective centers of module categories and quantum K-matrices
  • Time/place 10/2/2026, Friday, 12:10 pm (Easten time), Hill 705 (in person)
    
  • Abstract Braided monoidal categories have applications in various situations, in particular their universal R-matrices give solutions of the quantum Yang-Baxter equation and representations of braid groups of type A. There are powerful methods for constructing them: Drinfeld doubles of Hopf algebras and Drinfeld centers of monoidal categories. On the other hand, universal K-matrices and braided module categories, leading to solutions of the reflection equation and representations of braid groups of type B are much less well understood. We will describe a construction of reflective centers of module categories. It gives rise to braided module categories and a quantum double construction for universal K-matrices, thus completing Drinfeld's picture in type B. This is a joint work with Robert Laugwitz and Chelsea Walton.

• Speaker Qixuan Fang, Rutgers University at Newark
  • Title Meromorphic open-string vertex algebras, modules and a Dirac-like operator on spin manifolds
  • Time/place 10/16/2026, Friday, 12:10 noon (Easten time), Hill 705 (in person)
    
  • Abstract In this talk, we discuss a construction of a sheaf of boson-fermion meromorphic open-string vertex algebras and a sheaf of their canonically twisted modules from spinor bundles on a spin manifold. In particular, we realize the Dirac operator as a component of some special vertex operator when acting on ground spinors. This is joint work with Yi-Zhi Huang and Fei Qi. If time permits, we will discuss generalization of this construction to Courant algebroids, which includes the special case of realizing the (three-form twisted) de Rham differential as a vertex operator component on differential forms.

Some related talks

• Speaker Siddhartha Sahi, Rutgers University
  • Title The Opdam-Cherednik kernel is the Laplace transform of a positive measure
  • Event Mathematical Physics Seminar
  • Time/place 9/17/2026, Thursday, 12:10 pm (Easten time), Hill 705 (in person)
    
  • Abstract The trigonometric Calogero-Moser-Sutherland Hamiltonian associated with a root system R is the Schroedinger operator
    
    whose symmetric eigenfunctions, after gauging out the ground state, are the Heckman-Opdam hypergeometric functions F_{k,s}; the Opdam-Cherednik kernel is their nonsymmetric refinement. We prove that the Opdam-Cherednik kernel can be written as the Laplace transform of a positive measure supported on the convex hull of the Weyl group orbit of its argument. As a consequence, the trigonometric Dunkl intertwining operator is positivity preserving. The main ingredient in the proof is a new formula for the Opdam-Cherednik kernel as a degeneration of nonsymmetric Macdonald polynomials.
    Our results can be seen as a generalization of the work of Harish-Chandra and Kostant on integral formulas for spherical functions.
    As a further application, we prove majorization inequalities for Macdonald polynomials and Heckman--Opdam hypergeometric functions associated with arbitrary root systems.
    This is joint work with Colin McSwiggen (Academia Sinica), arXiv:2606.15185

• Speaker Yi-Zhi Huang, Rutgers University
  • Title Mathematical construction and study of conformal-field-theoretic tensor categories
  • Event Mathematical Physics Seminar
  • Time/place 10/15/2026, Thursday, 12:10 pm (Easten time), Hill 705 (in person)
    
  • Abstract Tensor categories now play an important role in the study of the representation theory of infinite-dimensional Lie algebras and other algebras related to two-dimensional conformal field theories. They have also been viewed as a type of generalized symmetries in physics (symmetry topological field theories) and are used to describe and study fractional quantum Hall systems, anyons, and other phenomena in condensed matter physics. Recently there are a lot of progresses in the general construction and study of tensor categories arising from the mathematical approaches to conformal field theories, especially in the representation theory of vertex operator algebras. I will discuss some of these main progresses and will also discuss the connection with the probability construction of the Liouville conformal field theory.

• Speaker Christoph Schweigert, University of Hamburg
  • Title On Graphical Calculi and Conformal Field Theory
  • Event Colloquium
  • Time/place 11/18/2026, Wednesday, 3:30 pm (Easten time), Hill 705 (in person)
    
  • Abstract Graphical calculi serve as powerful and efficient tools for studying (higher) algebraic structures. Through the idea of skein theory, they also play a fundamental role in the construction of topological field theories. In this talk, we introduce two different graphical calculi and demonstrate how they provide insights into the mathematical structure of two-dimensional conformal field theory.

Previous semesters