Lie Group/Quantum Math Seminar

Lie Group/Quantum Mathematics Seminar

Organizers Lisa Carbone, Yi-Zhi Huang, Jim Lepowsky and Siddhartha Sahi.

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, 2025

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 talks

  • Speaker Dennis Hou, Rutgers University
    • Title Lie theory over noncommutative rings (Ph.D.Thesis defense)
    • Time/place 3/27/2026, Friday, 1:00 noon (Easten time), Hill 705 (in person)
    • Abstract We review and extend the theory of Lie algebras over noncommutative rings (Kapranov 1998; Berenstein–Retakh 2008), introducing a Hopf-theoretic approach to Lie integration. We also explore the prospects for generalizing other representation-theoretic structures to the quaternionic setting.

All scheduled talks

  • Speaker Yi-Zhi Huang, Rutgers University
    • Title Cofiniteness and P(z)-tensor product bifunctors in orbifold theories associated to abelian but not-necessarily-finite groups
    • Time/place 2/6/2026, Friday, 12:10 pm (Easten time), Hill 705 (in person but also accessible online through Zoom)
      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
    • Abstract Let V be a Möbius vertex algebra and G an abelian group of automorphisms of V. We construct P(z)-tensor product bifunctors for the category of C_{n}-cofinite grading-restricted generalized g-twisted V-modules (without g-actions) for g in G and the category of C_{n}-cofinite grading-restricted generalized g-twisted V-modules with G-actions for g\in G. In this paper, an automorphism g of V can be of infinite order and does not have to act semisimply on V, and the group G can be an infinite abelian group containing nonsemisimple automorphisms of V.
    • Slides pdf file.
    • Archive paper arXiv:2601.12834

  • Speaker Geyang Dai, National University of Singapore
    • Title Elliptic Chern Characters and Elliptic Atiyah–Witten Formula
    • Time/place 2/20/2026, Friday, 12:10 pm (Easten time), Hill 705 (in person)
    • Abstract A principal G-bundle over a manifold X, equipped with a connection, together with a positive-energy representation, gives rise to a circle-equivariant gerbe module on the free loop space LX. From this data we construct an elliptic Chern character on LX, and a refinement, the elliptic Bismut–Chern character on the double loop space.

      We also generalize the Atiyah–Witten formula to double loop space. We show that the four Pfaffian sections, corresponding to the four spin structures on an elliptic curve, are identified with the four elliptic holonomies arising from the four virtual level one positive-energy representations when G=Spin. These constructions are closely related to conformal blocks in Chern–Simons gauge theory.
    • Archive paper arXiv:2601.18126

  • Speaker Darlayne Addabbo, The State University of New York Polytechnic Institute
    • Title Vertex operator algebras and associative algebras
    • Time/place 2/27/2026, Friday, 12:10 noon (Easten time), Hill 705 (in person)
    • Abstract Given a vertex operator algebra V, Zhu defined an associative algebra A(V) such that there is a one to one correspondence between irreducible admissible V-modules and irreducible A(V)-modules. Zhu’s algebra was subsequently generalized by Dong, Li, and Mason, who introduced higher level Zhu algebras. Higher level Zhu algebras are important tools in the study of irrational vertex operator algebras. More recently, given a VOA V, Huang defined a new associative algebra A^\infty(V) which contains the higher level Zhu algebras as subalgebras. In this talk, we will discuss progress we have made in studying these new algebras.

  • Speaker Daniel Tan, Rutgers University
    • Title On cofiniteness conditions and convergence in orbifold conformal field (Ph.D.Thesis defense)
    • Time/place 3/13/2026, Friday, 12:00 noon (Easten time), Hill 705 (in person and online through Zoom)
      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
    • Abstract The modules for a vertex operator algebra V can be twisted by an automorphism of V. Products of twisted intertwining operators among such twisted modules define correlation functions in orbifold conformal field theory as infinite series. We investigate under what conditions these correlation functions converge.

      Our results include a derivation of the twisted Knizhnik–Zamolodchikov equations and their generalization to general products of twisted intertwining operators among untwisted and twisted discretely graded C_1-cofinite modules. We introduce a notion of C_n-cofiniteness for twisted modules, and show that every finitely generated twisted V-module is C_n-cofinite, for all n > 0, if V is C_2-cofinite and of CFT type. We also prove that certain products of twisted intertwining operators among modules twisted by elements in a finite abelian group of automorphisms are convergent without the need for V to be C_2-cofinite.

  • Speaker Jishen Du, Rutgers University
    • Title Twisted intertwining operator, tensor product of twisted modules, and their associativity (Ph.D.Thesis defense)
    • Time/place 3/13/2026, Friday, 1:00 noon (Easten time), Hill 705 (in person and online through Zoom)
      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
    • Abstract We introduce the notion of twisted intertwining operators (intertwining operators among twisted modules) for a vertex operator algebra V. We give the skew-symmetry and contragredient isomorphisms between spaces of twisted intertwining operators and also prove some properties of twisted intertwining operators. Using twisted intertwining operators, we introduce a notion of P(z)-tensor product of two objects W_1 and W_2 in a category of g-twisted V-modules for g in a group G of automorphisms of V. We give a set-theoretic construction of the P(z)-tensor product, where the contragredient module of the P(z)-tensor product module can be realized as a subspace of the dual space of the vector space tensor product of W_1 and W_2. We find a criterion for an element in this dual space to be in the contragredient module of the P(z)-tensor product module. Using the set-theoretic construction and the criterion, we prove that when a category of twisted modules satisfies suitable conditions, the associativity for twisted intertwining operators among objects in the category holds. As a result, we construct an associativity isomorphism for the P(z)-tensor product bifunctor in a suitable sense.

  • Speaker Dennis Hou, Rutgers University
    • Title Lie theory over noncommutative rings (Ph.D.Thesis defense)
    • Time/place 3/27/2026, Friday, 1:00 noon (Easten time), Hill 705 (in person)
    • Abstract We review and extend the theory of Lie algebras over noncommutative rings (Kapranov 1998; Berenstein–Retakh 2008), introducing a Hopf-theoretic approach to Lie integration. We also explore the prospects for generalizing other representation-theoretic structures to the quaternionic setting.

  • Speaker Martin Andler, Université de Versailles St-Quentin
    • Title
    • Time/place 4/24/2026, Friday, 12:10 pm (Easten time), Hill 705 (in person)
    • Abstract

Previous semesters