Radu Toma

I am a post-doc at Institut de mathémathiques de Jussieu IMJ-PRG, working in the Automorphic Forms group with Farrell Brumley, funded by a Cofund MathInGreaterParis fellowship.

Research interests: automorphic forms in higher rank and the sup-norm problem and other topics in number theory, geometry of numbers, cryptography.

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 etc.

• The sup-norm problem for automorphic forms in higher rank,
  Doctoral thesis, University of Bonn. It's the two papers above plus a useful introduction, I hope. [ 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 ]

Current & Upcoming Activities

• Talk at Séminaire d'Arithmétique à Lyon
  November 16th 2024

Past Activities

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

• Talk at the Renyi Number Theory Seminar
  Budapest, 7.03.2024

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

• 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)

• 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.

• 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