Lie Group/Quantum Math Seminar

Lie Group/Quantum Mathematics Seminar

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

Time Friday, 12:00 to 1:00 pm.

Place Hill 705.

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. This seminar also has a page Lie Groups Quantum Mathematics Seminar, maintained by 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 and Colloquia page.

Fall, 2019

  • Speaker Sven Moeller, Rutgers University
    • Title Bounds for the constant terms of weight-0 vector-valued modular forms and generalized deep holes of the Leech lattice vertex operator algebra
    • Time/place 9/20/2019, Friday, 12:00 in Hill 705
    • Abstract We derive an upper bound for (the sum corresponding to an isotropic subgroup of) the constant terms of a weight-0 vector-valued modular form that transforms under the Weil representation, based on a pairing argument with weight-2 vector-valued Eisenstein series.

      As an application we prove a vertex algebra analogue of the remarkable result by Conway, Parker and Sloane (and Borcherds) that there is a bijection between the deep holes of the Leech lattice and the 23 Niemeier lattices with roots.

  • Speaker Angela Gibney, Rutgers University
    • Title On factorization and vector bundles of conformal blocks from vertex algebras
    • Time/place 10/11/2019 (to be adjusted), Friday, 12:00 in Hill 705
    • Abstract Modules over conformal vertex algebras give rise to sheaves of coinvariants and conformal blocks on moduli of stable pointed curves. We show that under certain natural hypotheses, these sheaves satisfy the factorization property, a reflection of their inherent combinatorial nature. As an application, we prove they are vector bundles. These provide a generalization of vector bundles defined by integrable modules over affine Lie algebras at a fixed level. Satisfying factorization is essential to a recursive formulation of invariants, like ranks and Chern classes, and to produce new constructions of rational conformal field theories.

  • Speaker Jinwei Yang, University of Alberta
    • Title
    • Time/place 10/14/2019, Monday, 3:20 pm (Note the special time)
    • Abstract

  • Speaker Si Li, Tsinghua University and IAS
    • Title
    • Time/place 11/8/2019, Friday, 12:00 in Hill 705
    • Abstract

  • Speaker Abid Ali,
    • Title
    • Time/place 11/15/2019, Friday, 12:00 in Hill 705
    • Abstract

  • Speaker Shashank Kanade, University of Denver
    • Title
    • Time/place 12/6/2019, Friday, 12:00 in Hill 705
    • Abstract

Previous semesters