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.

Spring, 2024

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.

  • Speaker Shaobin Tan, Xiamen University
    • Title Toroidal Extended Affine Lie Algebras and Integrable Representations
    • Time/place 1/26/2023, Friday, 12:10 pm (Eastern Time), Hill 705 (in person)
    • Abstract The extended affine Lie algebras (EALAs for short) are generalization of the finite dimensional simple Lie algebras and affine Kac-Moody algebras over the field of complex numbers, and the toroidal EALAs are a class of the most important EALAs. In this talk, we deal with the classification of irreducible integrable representations for the elliptic Lie algebras, i.e. the toroidal EALAs of nullity two.

  • Speaker Terence Coelho, Rutgers University
    • Title New perspectives on fixed point subalgebras of affine Lie algebras corresponding to Dynkin diagram automorphisms
    • Time/place 3/20/2023, Wednesday, 11:45 am (note the special day and time), Hill 705 (in person)
    • Abstract We present new realizations of the simply-laced affine Lie algebras that do not distinguish any node in the affine Dynkin diagram, which allows one to more easily study the fixed-point subalgebras corresponding to affine Dynkin diagram automorphisms. We show how these fixed-point subalgebras compare to the associated non-simply-laced affine Lie algebras, and present an alternative classification of affine root systems and affine Lie algebras from this perspective. Finally, we discuss the corresponding realizations of the level-one irreducible highest weight modules for a simply-laced affine Lie algebra and how the affine Dynkin diagram automorphisms can be lifted to their direct sum.

  • Speaker Lea Beneish, University of North Texas
    • Title Moonshine modules and a question of Griess
    • Time/place 3/22/2023, Friday, 12:10 pm (Eastern Time), Zoom link above (online)
    • Abstract Recent work on monstrous moonshine has shown that there are exact formulas for the multiplicities of the irreducible components of the moonshine modules, showing in particular that these multiplicities are asymptotically proportional to the dimensions. With the recent proof of the umbral moonshine conjecture it is natural to ask whether this distribution result extends to other instances of moonshine, including umbral moonshine. We consider the general situation in which a finite group acts on an infinite-dimensional graded module in such a way that the graded-trace functions are weakly holomorphic modular forms. Under some mild hypotheses we completely describe the asymptotic module structure of the homogeneous subspaces. As a consequence, we find that moonshine for a group gives rise to partial orderings on its irreducible representations. This serves as a first answer to a question posed by Griess. This talk is based on joint work with Victor Manuel Aricheta.

  • Speaker Hofie Hannesdottir, Institute for Aavanced Study

  • Speaker Hong Chen, Rutgers University
    • Title Binomial Coefficients and Littlewood-Richardson Coefficients for Interpolation Polynomials
    • Time/place 4/3/2023, Wednesday, 11:45 noon (note the special day and time), Hill 705 (in person)
    • Abstract Interpolation Jack and Macdonald polynomials were introduced by Knop--Sahi and Okounkov in the 90s, defined by certain degree and interpolation conditions. The evaluations of interpolation polynomials are called binomial coefficients. I will talk about some recent work on these binomial coefficients: they are positive and monotone. As an application, we show that this gives a characterization of the containment partial order in terms of Schur positivity or Jack positivity; this result is in parallel with the work of Cuttler--Greene--Skandera--Sra and Khare--Tao, which gave characterizations of two other partial orders, namely, majorization and weak majorization. Time permitting, I will present a new combinatorial formula for the Littlewood--Richardson coefficients and some positivity results.

      This is joint work with my advisor, Prof. Siddhartha Sahi.

  • Speaker Eric Schippers, University of Manitoba
    • Title
    • Time/place 4/5/2023, Friday, 12:10 noon (Eastern Time), Hill 705 (in person)
    • Abstract

  • Speaker Jishen Du, Rutgers University
    • Title
    • Time/place 4/26/2023, Friday, 12:10 noon (Eastern Time), Hill 705 (in person)
    • Abstract

Previous semesters