Aritra Bhattacharya
I am currently a postdoc at Beijing International Center for Mathematical Research, Peking University, under the mentorship of Prof. Yibo Gao. I completed my Ph.D. in mathematics from the Institute of Mathematical Sciences, Chennai, India in April 2024. My Ph.D. supervisor was Prof. S. Viswanath.
My research focuses on Algebraic Combinatorics, with a central theme of understanding relations between families of symmetric functions and establishing positivity results. I work primarily with Macdonald polynomials and their specializations (Hall-Littlewood and q-Whittaker functions), as well as LLT polynomials. To study these objects, I employ combinatorial models involving Young tableaux and Dyck paths, alongside algebraic tools from finite, affine, and double affine Hecke algebras and the representation theory of Kac-Moody Lie algebras.
Recently, I have engaged with Kazhdan-Lusztig theory, incorporating geometric techniques from the theory of perverse sheaves to prove a generalization of the classical Kazhdan-Lusztig positivity theorems. I regularly use computer programming tools such as SageMath to experiment and formulate conjectures.
Preprints and Publications
- On factorization of matrix of Kazhdan-Lusztig polynomials arXiv:2602.19508
- A tableaux formula for q-rook numbers arXiv:2507.00766
- Equating Inv-Quinv formulas for the q-Whittaker and modified Hall-Littlewood functions arXiv:2412.09929
- q-Whittaker polynomials: bases, branching and direct limits arXiv:2412.00116
- The monomial expansion formula for Hall-Littlewood P-polynomials arXiv:2407.14652
- Monomial expansions for q-Whittaker and modified Hall-Littlewood polynomials arXiv:2311.07904
- Clebsch-Gordan coefficients for Macdonald polynomials arXiv:2310.10846
- Haglund's positivity conjecture for multiplicity one pairs arXiv:2205.11802