Research and publications

My research work is related to dynamical systems and geometric analysis. I’m especially interested in the interplay between ergodic theory and spectral theory.

In particular, i’ve been studying Ruelle resonances of hyperbolic systems, resonances of the Laplacian on hyperbolic manifolds or other chaotic models.

The mathematical techniques i have been using include complex analysis, representation theory, thermodynamical formalism, additive combinatorics and more recently free probability and random matrices. For a recent article of Quanta Magazine explaining some of the work i’m related to, see here.

My full list of publication is available here

Recent preprints and papers (since 2018):

  • F. Naud, Determinants of Laplacians on Random Hyperbolic surfaces (2023). Arxiv preprint.
  • F. Naud and Polyxeni Spilioti, On the spectrum of twisted Laplacians and the Teichmüller representation (2022). Arxiv preprint.
  • F. Naud, Random covers of compact surfaces and smooth linear spectral statistics (2022). Arxiv preprint.
  • Michael Magee and F. Naud, Extension of Alon’s and Friedman’s conjectures to Schottky surfaces (2021). Arxiv preprint.
  • Michael Magee, F. Naud and Doron Puder, A random cover of a compact hyperbolic surface has relative spectral gap 3/16−ε. Geom. Funct. Anal. 32 (2022), no. 3, 595-661. Arxiv preprint.
  • Jialun Li, F. Naud and Wenyu Pan, Kleinian Schottky groups, Patterson-Sullivan measures and Fourier decay. Duke Math. J. 170 (2021), no. 4, 775–825.
  • Michael Magee and F. Naud, Explicit spectral gaps for random covers of Riemann surfaces. Publ. Math. Inst. Hautes Études Sci. 132 (2020), 137–179.
  • F. Naud, Hyperbolic dynamics meets Fourier analysis, book review of V. Baladi, dynamical zeta functions and dynamical determinants for hyperbolic maps, a functional approach. Jahresber. Dtsch. Math.-Ver. 122 no 4, 263-268 (2020).
  • Dmitry Jakobson, F. Naud and Louis Soares. Large degree covers and sharp resonances of hyperbolic surfaces. Ann. Inst. Fourier (Grenoble) 70 (2020), no. 2, 523–596.
  • F. Naud, On the rate of mixing of circle extensions of Anosov maps. J. Spectr. Theory 9 (2019), no. 3, 791–824.
  • F. Naud, Anke Pohl and Louis Soares, Fractal Weyl bounds and Hecke triangle groups. Electron. Res. Announc. Math. Sci. 26 (2019), 24–35.
  • Oscar Bandtlow and F. Naud, Lower bounds for the Ruelle spectrum of analytic expanding circle maps. Ergodic Theory Dynam. Systems 39 (2019), no. 2, 289–310.

Courses notes and other:

  • Notes on Hecke operators and spectral gaps for SU2(C). File.pdf
  • An introduction to Dolgopyat’s method, course notes.
  • My habilitation thesis (in french). File.pdf
  • A Bourbaki seminar on Fractal Weyl laws, 2015. Notes here.