You've found the homepage of Songhao Zhu at the School of Mathematics, Georgia Institute of Technology.
Research
Interests: Representation Theory & Algebraic Combinatorics, Lie Superalgebras, Representation Theory in general. I look forward to exploring broader impacts of these subjects.
I am a Visiting Assistant Professor at Georgia Tech working with Plamen Iliev. I received my Ph.D. from Rutgers University, where I worked under the supervision of Siddhartha Sahi.
Current CV
Current Research Statement
Upcoming Talk
- UGA Algebra Seminar, Athens, GA
- Time: Oct. 12, 4:30-5:30 PM
- Title: From Shimura operators to the integrability of Calogero-Moser-Sutherland operators
- Abstract: We discuss super Shimura operators associated with Hermitian symmetric superpairs and their relationship to type BC supersymmetric interpolation polynomials. In a different direction, Heckman–Opdam theory establishes the quantum complete integrability of Calogero–Moser–Sutherland operators arising in quantum mechanics. In the non-super setting, the commutativity of Shimura operators, and thus of their radial parts, suggests an alternative way of proving such integrability. By bypassing geometry, we propose a conjectural, purely algebraic approach to this problem in both the ordinary and super settings. We will share recent developments.
- Slides
Research Works
- In progress: Integrability of CMS systems via Shimura operator theory
- Super Krawtchouk Polynomials via Lie Superalgebras (with Plamen Iliev) (ArXiv)
- Eigenvalues of Supersymmetric Shimura operators and interpolation polynomials (with Siddhartha Sahi) (Adv. in Math.) (slides)
- Shimura operators for certain Hermitian symmetric superpairs (Journal of Lie Theory) (slides)
- Growth of root multiplicities along imaginary root strings in Kac–Moody algebras (with Lisa Carbone, Terence Coelho, Scott H. Murray, and Forrest Thurman) (Comm. in Alg.)
- A vanishing theorem for the canonical blow-ups of Grassmann manifolds (with Hanlong Fang) (Complex Manifolds),
