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. From April 2017 to July 2017 I visited Igor Wigman at the Department of Mathematics, King’s College London. From October 2017 I am a postdoctoral researcher at CEMPI, Lille and Université Lille 1 – Sciences et Technologies, supervised by Nicole Raulf.
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. (to appear in Revista Matemática Iberoamericana, arXiv)
4. Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space. (with O. Balkanova, G. Cherubini, D. Frolenkov and N. Laaksonen), (to appear in Transactions of the American Mathematical Society, arXiv)
1. Second moments of symmetric square L-functions. (with Min Lee)
2. Quantum Variance of Hecke-Maass forms for Bianchi groups. (with Nicole Raulf)