Research

Research interests

Automorphic forms, Spectral theory, Analytic number theory

My research interests lie on problems related to L-functions of Maass forms, Quantum Unique Ergodicity and equidistribution problems. I am also interested on  various counting problems in the spectral theory of automorphic forms, such as Prime Geodesic theorems and Lattice counting problems.

I finished my PhD in Pure Mathematics at UCL, UK under the supervision of Yiannis Petridis. In my thesis I worked on two different 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.

Papers

1. On the distribution of lattice points on hyperbolic circles. (with Pär Kurlberg, Stephen Lester and Igor Wigman), (submitted for publication, arXiv)

2. Quantum ergodicity in shrinking balls of arithmetic hyperbolic manifolds. (with R. Frot and N. Raulf), (submitted for publication, arXiv)

3. Second Moment of the Prime Geodesic Theorem for PSL(2,Z[i]). (with G. Cherubini and N. Laaksonen), (submitted for publication, arXiv)

4. CM-points and lattice counting on arithmetic compact Riemann surfaces. (with M. Alsina),  J. Number Theory 212, 2020, 339–353. (arXiv)

5. Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space. (with O. BalkanovaG. Cherubini, D. Frolenkov and N. Laaksonen), Trans. Amer. Math. Soc. 372 (2019), no. 8, 5355–5374. (arXiv)

6. Mean value and Ω-results for the hyperbolic lattice point problem in conjugacy classes. Rev. Mat. Iberoam. 35 (2019), no. 4, 1123–1152. (arXiv)

7. Ω-results for the hyperbolic lattice point problem. Proc. Amer. Math. Soc., vol. 145 (2017), no. 4, 1421–1437. (arXiv)

8. The hyperbolic lattice point problem in conjugacy classes. (with Y. Petridis), Forum Math. 28 (2016), no. 5, 981–1003. (arXiv)

Others

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)