Radu Toma

New website

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

• Defence 16th of September, 16:00, Großer Hörsaal, Wegelerstr. 10. You can check out my thesis here.

Past Activities

• Workshop Distribution of orbits: Arithmetics and Dynamics
  Switzerland, 8.07 - 12.07.2024

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

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

• 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.

Contact

Radu Toma
Mathematisches Institut
Endenicher Allee 60
53115 Bonn, Germany

Office: N1.009
E-Mail: toma (at) math.uni-bonn.de