Research

Research Interests

My research is rooted in Pure Mathematics, specifically focusing on the intersection of Algebra, Analysis, and Representation Theory, with active applications and motivations drawing from Quantum Mechanics and Number Theory.

My current work is focused across three primary, overlapping areas:

Deformations, Dualities, and Dirac Operators: My research focuses on algebraic deformations of classical dualities together with the construction of Dirac operators for graded algebras and classification of (unitary) irrreducible modules.

Harmonic Analysis and the Langlands Programme: Stemming from my early work, I study the spherical automorphic spectrum, residue distributions, and explicit computations within the Langlands correspondence (such as the Langlands correspondence for tori).

Feel free to browse my full list of papers in the Publications page or explore open-source implementations of related mathematical frameworks under Algorithms.

Future Directions

My upcoming research program operates at the intersection of established algebraic frameworks and emerging quantum technologies. Moving forward, my goals are twofold:

Deformed Dualities & The Langlands Programme: I will continue my core investigations into deformed algebraic dualities (such as Dunkl-Cherednik and quantum groups deformations) and explicit formulations within the Langlands programme, exploring how these deep geometric structures connect back to representation theory.

Quantum Information Theory: I am currently expanding my research toward quantum information. My immediate focus is on identifying structural problems where classical tools from representation theory, harmonic analysis, and algebraic dualities can offer new insights into quantum states and channels.