Research Interest
My research is in algebraic combinatorics, with a focus on symmetric functions and diagonal harmonics, as well as tableaux, poset structures, and related combinatorial and representation-theoretic models, often using a combination of combinatorial, algebraic, and computational approaches.
Selected Research Projects
The following projects highlight some of my current research directions and ongoing work.
Stable Tamari Lattices
Catalanimals
Vacillating Tableaux
Immaculate Hecke Posets
This project studies the combinatorial and structural properties of stable Tamari lattices and related posets.
A central goal is to explore their connection to multivariate diagonal harmonics and related symmetric function theory.
This project develops combinatorial and algebraic tools for studying objects related to diagonal harmonics, including LLT-type series, nonsymmetric Hall-Littlewood polynomials, and aspects of Macdonald theory.
The goal is to connect algebraic, geometric, and combinatorial perspectives through explicit constructions.
This project studies vacillating tableaux as walks on Young’s lattice and their connections to the partition algebra.
A central goal is to understand how these objects relate to integer sequences and Young tableaux through bijections and RSK-type constructions, as well as their links to crossings and nestings of set partitions.
This project studies skew immaculate functions and skew dual immaculate functions, which extend Schur-type ideas from symmetric functions to the quasisymmetric setting, together with the associated 0-Hecke posets.
The goal is to understand the combinatorial and structural properties of these posets and their connections to the underlying algebraic theory.
Selected Research Activities
-
AIM SQuaRE (2024 - 2026): Vacillating Tableaux
​
-
IAS Research Community in Algebraic Combinatorics (2025): Skew Extended 0-Hecke Poset
​
-
AMS-MRC Algebraic Combinatorics (2024): Stable Tamari Lattices​
​
-
BIRS-Banff Community in Algebraic & Enumerative Combinatorics (2024): Skew Immaculate Hecke Poset ​
​
-
Collaborate@ICERM:
Stable Tamari Lattices (2025), Macdonald Polynomials and Catalanimals (2024), Vacillating Tableaux (2023, 2024)