Radu Toma

I am a fourth-year doctoral student in the Analytic Number Theory and Automorphic Forms group at the University of Bonn, under the supervision of Prof. Dr. Valentin Blomer. I am particularly interested in automorphic forms in higher rank and the sup-norm problem, but also more classical number theory.
Starting autumn 2024 I'll be a postdoc in Paris with Farrell Brumley.
Here is my CV. You can reach me at
toma 🙈 math.uni-bonn.de

Publications and preprints

The sup-norm problem for newforms of large level on PGL(n),
Arxiv preprint: https://arxiv.org/abs/2401.02741

Hybrid bounds for the sup-norm of automorphic forms in higher rank,
Trans. Amer. Math. Soc. 376 (2023),
Arxiv preprint: https://arxiv.org/abs/2111.09923

Estimates for representation numbers of binary quadratic forms and Apollonian circle packings,
Journal of Number Theory, vol. 214, September 2020, pp. 399–413, doi:10.1016/j.jnt.2020.03.005
[ preprint ]

Notes

Atkin-Lehner operators for GL(n) * now part of my paper The sup-norm problem for newforms of large level on PGL(n),
This note explains how we may generalise the classical definition of Atkin-Lehner operators to GL(n) for n > 2. In particular, it contains a proof that the normaliser of the Hecke congruence group is trivial for n > 2, a definition for the Fricke involutions, and the (unfortunate) conclusion that there are no other Atkin-Lehner operators in these cases. [ pdf ]

The spectral theory of automorphic forms on SL(2, Z),
Part III Essay, University of Cambridge. This essay presents a proof of the spectral theorem for SL(2, Z). [ pdf ]

The arithmetic of binary quadratic forms,
Bachelor's thesis, Georg-August-Universität Göttingen. This thesis presents the theory of binary quadratic forms with a focus on representation numbers, non-fundamental discriminants, and an application to Apollonian circle packings. [ pdf ]

Comments and suggestions for any of my writings are very welcome!

Current & Upcoming Activities

Organising HCM career event for docs and postdocs: April 19th!

Talk at the Texas A&M Number Theory Seminar
Online, 26.03.2024

Past Activities

Talk at the Renyi Number Theory Seminar
Budapest, 7.03.2024

Number theory learning seminar on the modern ergodic method for proving equidistribution results
Uni Bonn, WS23/24

Talk at the Copenhagen Number Theory Seminar
Zoom, 11.12.2023

Automorphic Forms and L-functions of higher rank
London, 11-15.09.2023

Talk at Y-RANT
Cambridge, 06-08.09.2023

Analysis of Automorphic Forms and L-Functions in Higher Rank
Oberwolfach, 08.05-02.06.2023

Talk at Arithmetic Statistics in Automorphic Forms and Analytic Number Theory
Lausanne, 05-09.06.2023

Talk at the Number theory seminar of ETH Zürich,
Zürich, 28.10.2022

Research stay at EPFL, Chair of Analytic Number Theory,
Lausanne, September - December 2022

Talk at Building Bridges 5,
Sarajevo, 09.08.2022
On the sup-norm of automorphic forms in higher rank

Talk at the Workshop for Young Researchers in Mathematics, Simion Stoilow Institute of Mathematics of the Romanian Academy,
online, 05.05.2022
On the sup-norm of automorphic forms

Talk (recorded) at the Renyi Automorphic Forms Seminar,
online, 05.05.2022
Hybrid bounds for the sup-norm of automorphic forms in higher rank (slides)

Talk at ENTR Seminar,
online, 20.04.2022
On the sup-norm of automorphic forms

Co-organised a conference, Young Scholars in the Analytic Theory of Numbers and Automorphic Forms, 28-29 March 2022, at the University of Bonn, for doctoral students and postdocs.

Talk at Cambridge Junior Algebra/Number Theory seminar,
online, 4.02.2022
How loud is an arithmetic drum?

Talk at Laboratoire Paul Painlevé, Seminaire d'Arithmétique & study group on L-functions
Lille, 21.10.2021
Estimates for binary quadratic forms and Appollonian circle packings

Studentischer Vertreter im Vorstand des Mathematischen Instituts, 2021-2022

TA for Einführung in die Algebra, WS 21/22

Video for 3blue1brown's Sommer of Math Exposition:
The video explains in an accessible way (high-school / first-year uni level) how roots of unity and cyclotomic polynomials can help us solve a problem about comparing weights of several objects simultaneously.