In my thesis I worked on hyperbolic lattice counting problems. The classical hyperbolic lattice point problem is the hyperbolic analogue of the Gauss’ circle problem. I studied various modifications of it, as well as arithmetic applications of them.
You can find my thesis here.
My research focuses on the spectral theory of GL(2)-automorphic forms. My current research interests lie on problems related to L-functions of Maass forms and Quantum Unique Ergodicity. I am also interested on various counting problems in the spectral theory of automorphic forms, such as Prime Geodesic theorems and Lattice counting problems.
From October 2016 to March 2017 I visited Andrew Booker at the School of Mathematics in the University of Bristol with an LMS Postdoctoral Mobility Grant.
I am also a reviewer for Zentralblatt MATH.
Finally, here is my profile in Google Scholar.
Automorphic forms, Spectral theory, Analytic number theory
2. Ω-results for the hyperbolic lattice point problem. Proc. Amer. Math. Soc., vol. 145 (2017), no. 4, 1421–1437. (arXiv)
3. Mean value and Ω-results for the hyperbolic lattice point problem in conjugacy classes. Rev. Mat. Iberoam. 35 (2019), no. 4, 1123–1152. (arXiv)
1. The error term in term in the Prime Geodesic Theorem for hyperbolic 3-manifolds, (short review article in the Proceedings of the 16th Panhellenic Conference on Mathematical Analysis)