Grants and Contributions:

Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023)

My research forms part of the Langlands program, a branch of mathematics involving deep connections
between number theory, automorphic forms, representation theory, and algebraic geometry. I study the properties
of representations of certain matrix groups known as reductive p-adic groups. These matrix groups are defined in
terms of number theory - the matrix entries belong to p-adic fields - these fields are nonarchimedean completions of number
fields (finite extensions of the rational numbers). In recent years, there has been considerable interest in harmonic analysis
on p-adic symmetric varieties and connections with the Langlands program. My work involves
the study and construction of distinguished representations of reductive p-adic groups. These distinguished representations
exhibit specific symmetry properties relative to the involution that defines the p-adic symmetric space.
The basic building blocks in the theory of distinguished representations are the so-called relatively supercuspidal
representations. My main focus is on construction of relatively supercuspidal representations and the study of their properties,
particularly those that are relevant to the Langlands program.