My mathematical research interests are broad; they include analytic number theory, automorphic forms, equidistribution theory, and several other topics. The problems I work on are often related to geometric and arithmetic questions on modular surfaces and their generalizations, frequently involving counting problems in hyperbolic groups. The tools I a use are often analytic in nature using the theory of automorphic forms and their L-functions in an essential way. Many of the questions I investigate arise from the interplay between classical and quantum physical phenomena.
Some of the highlights in my research concern
- Improvements on classical error estimates in arithmetic cases of the hyperbolic lattice counting problem and its generalizations.
- Understanding the distribution of modular symbols and their generalizations.
- Obtaining higher order Fermi-conditions for the destruction of Maass forms.
- Understanding angular distributions in hyperbolic lattices and their generalizations.
This type of research falls under the category of basic research with no immediate real-world applications currently known. Sometimes referred to as blue sky research, it is driven by a fundamental desire to expand our scientific understanding. Historically, many topics such as electricity, atomic theory, genetics, and prime numbers were considered purely theoretical, yet today the understanding made by the basic researchers of the past, play an essential role in our everyday lives in everything from computers, medicine, transportation, and many other areas.
You can have a look at my reseach in my publication list