Lie Group/Quantum Math Seminar

Lie Group/Quantum Mathematics Seminar

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

Time Friday, 11:00 am to 12:00 noon (Eastern time).

Place Online via Zoom for Fall, 2021 until further notice (see below for the Zoom link and passcode).

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, 2021

Seminar talks in this semester will still be online using zoom until further notice.

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

Most of the talks will be recorded and will be placed in the YouTube channel Rutgers Lie Groups Quantum Math Seminar

  • Speaker Lisa Carbone, Rutgers University
    • Title Imaginary reflections and discrete symmetries in the Heterotic Monster
    • Time/place 9/17/2021, Friday, 11:00 am (Eastern Time), Zoom link above
    • Abstract We give an interpretation of certain symmetries of the root system of the monster Lie algebra m, and more generally the infinite family of monstrous Lie algebras m_g, one for each g in the Monster finite simple group M, in terms of discrete symmetries of the heterotic string compactified to 0 + 1 dimensions. We show that a certain discrete symmetry of the monster Lie algebra can be extended to a discrete symmetry of a supersymmetric index Z which counts (with signs) the number of BPS-states. The imaginary reflection permutes two sets of BPS states labeled by imaginary roots up to a minus sign. This is joint work with Natalie Paquette.

  • Speaker Yi-Zhi Huang, Rutgers University
    • Title Representation theory of vertex operator algebras and conformal field theory
    • Time/place 10/1/2021, Friday, 11:00 am (Eastern Time), Zoom link above
    • Abstract A program to construct weakly and full conformal field theories in the sense of Segal using the representation theory of vertex operator algebras was started more than 30 years ago. After more than 30 years, major progresses have been made and many problems in this program have been solved. In this talk, I will review the history of and the major progresses in this program and will also discuss the current status of this program.

  • Speaker Cristian Lenart, SUNY Albany
    • Title A combinatorial Chevalley formula for semi-infinite flag manifolds and related topics
    • Time/place 10/8/2021, Friday, 11:00 am (Eastern Time), Zoom link above
    • Abstract

  • Speaker Robert McRae, Tsinghua University
    • Title
    • Time/place 10/15/2021, Friday, 11:00 am (Eastern Time), Zoom link above
    • Abstract

Some additional talks by members of this seminar

  • Speaker Yi-Zhi Huang, Rutgers University
    • Title Representation theory of vertex operator algebras and conformal field theory
    • Event The Mathematics of Conformal Field Theory II, Mathematical Sciences Institute, Australian National University
    • Time 7/6/2021, Tuesday, 9:15 am (Australian Eastern Standard Time) or 7/5/2021, Monday, 7:15 pm (Eastern time)
    • Location The conference is entirely online. Registered participants can access the Zoom links through the SharePoint page. Registration is free for online participants
    • Abstract A program to construct weakly and full conformal field theories in the sense of Segal using the representation theory of vertex operator algebras was started more than 30 years ago. After more than 30 years, major progresses have been made and many problems in this program have been solved. In this talk, I will review the history of and the major progresses in this program and will also discuss the current status of this program.

  • Speaker Yi-Zhi Huang, Rutgers University
    • Title Associative algebras and intertwining operators
    • Event Subfactors, Vertex Operator Algebras, and Tensor Categories, the Institute for Advanced Study in Mathematics, Zhejiang University, Hangzhou, China
    • Time 9/22/2021, Wednesday, 8:00 pm (Eastern Time) or 9/23/2021, Thursday, 8:00 pm (Beijing time)
    • Location The conference is entirely online. The videos of most of the talks will be posted in the bottom of this page after the talks.
    • Abstract The connection between intertwining operators and A(V)-module maps (where A(V) is the Zhu algebra associated to a vertex operator algebra V) is needed in the last step of my proof of the Moore-Seiberg conjecture on the modular invariance of intertwining operators for rational conformal field theories. In this talk, I will discuss my recent work proving that the spaces of (logarithmic) intertwining operators are isomorphic to suitable spaces of module maps between suitable modules for the associative algebras A^∞(V) and A^N(V) that I introduced last year. The main motivation of this work is to give the last step of the proof of the modular invariance of (logarithmic) intertwining operators when V is C_2-cofinite but might not be reductive.

A conference with talks given by members of this seminar

Previous semesters