My research explores the representation theory of connected reductive groups over non-archimedean local fields — a field rich with connections to number theory, harmonic analysis, and algebraic geometry. I'm particularly focused on branching problems for irreducible smooth representations, shedding light on how representations behave when restricted to subgroups. 

📄 Download my Research Statement

 PhD Thesis (submitted)

Branching rules for  all  irreducible smooth representations of unramified U(1,1)
 Supervisor: Dr Monica Nevins

In my doctoral thesis, I prove that for the rank-one quasi-split unitary group G, the restriction of all irreducible smooth representations of G to a maximal compact subgroup K is multiplicity-free, characterised by distinct depth and degree, up to scaling by a quasi-character of  G. The decomposition is given in terms of explicit irreducible representations of K that I construct. Moreover, I show that in a neighbourhood of identity, the decomposition is governed by representations constructed using nilpotent elements in the Lie algebra of G, thereby proving a new case of a recent conjecture.

 Broader Research Goals:

Past Projects & Internships: