Claire Burrin

Assistant Professor
University of Zurich
Institute of Mathematics
Winterthurerstrasse 190
8057 Zürich, Switzerland

Office: Y27K26
Tel.: +41 44 635 58 86

My research is in number theory, and its connections with geometry and dynamics. I am in particular interested in counting and equidistribution problems, automorphic forms, and spectral methods. Before joining UZH, I was a senior research associate at ETH (Oberassistentin) and a Hill assistant professor at Rutgers University.


  • Spring 2023: Complex analysis
  • Fall 2022: Spectral theory of hyperbolic surfaces (CUSO Graduate Lectures in Berne for the Swiss Doctoral Program)
  • Spring 2022: Topics in number theory: L-functions and modular forms
  • Beware: These notes have not been revised - they will contain typos

  • Publications, preprints, and work in preparation

  • On the nonmultiplicativity of Fourier coefficients of cusp forms. In preparation.
  • Rational points on spheres, with Matthias Gröbner. In preparation (2023).
  • Pairs in discrete lattice orbits with applications to Veech surfaces, with Samantha Fairchild and an appendix by Jon Chaika. Submitted (2022).
  • Windings of prime geodesics, with Flemming von Essen. Submitted (2023).
  • The Manin-Drinfeld theorem and the rationality of Rademacher symbols.
  • Journal de Théorie des Nombres de Bordeaux 34 (3) (2022), 739-753.
  • Translates of rational points on expanding horocycles on the modular surface, with Uri Shapira, Shucheng Yu.
  • Mathematische Annalen 382 (2022), 655-717.
  • Infinitely many twin prime polynomials of odd degree, with Matthew Isaac.
  • The American Mathematical Monthly 128 (2021), no. 10, 929-935.
  • Effective counting for discrete lattice orbits in the plane via Eisenstein series, with Amos Nevo, Rene Rühr, Barak Weiss. L'Enseignement Mathématique 66 (2020), no. 3-4, 259-304.
  • Transformation laws for generalized Dedekind sums associated to Fuchsian groups, with Jay Jorgenson, Cormac O'Sullivan, Lejla Smajlović. Acta Arithmetica 196, no.2, 2020.
  • Dedekind sums, reciprocity, and non-arithmetic groups.
  • Contemporary Mathematics 732, 2019.
  • Reciprocity of Dedekind sums and the Euler class.
  • Proceedings of the American Mathematical Society 146, no.4, 2018.
  • Generalized Dedekind sums and equidistribution mod 1.
  • Journal of Number Theory 172, 2017.
  • Dedekind symbols and applications of the spectral theory of Kloosterman sums.
  • Dissertation ETH No. 23634, 2016. ETH medal for outstanding thesis.

    Conferences and seminars

    I am part of the Zurich Dynamics and Ergodic Theory group and a co-organizer of the joint Ergodic Theory and Dynamical Systems Seminar between ETH and UZH.
    This year I am also co-organizing with Yingkun Li, Christina Roehrig and Riccardo Zuffetti the online international seminar on automorphic form, taking place Tuesdays 16-17h (CET). Website here!
    Alessandra Iozzi, Michah Sageev and I are organizing the next edition of Ventotene on Groups and Rigidity in the Zimmer Program (GRAZP), September 11-16 2023
    Corinna Ulcigrai and I just organized this year's Swiss Mathematical Society autumn conference on Dynamics and Groups at UZH, September 14-16, 2022

    Recent & upcoming talks

  • Nov 23-25, 2022: Stochastic geometry workshop, Osnabrück
  • Dec 8-9, 2022: Crosscurrents in number theory, analysis and geometry, Paris 13
  • Feb 23, 2023: Number theory seminar, Basel
  • Mar 3, 2023: Séminaire de géométrie, Bordeaux
  • Mar 9, 2023: Séminaire de géométrie et topologie de Marseille
  • Apr 5, 2023: Algebraic geometry and number theory seminar, Chalmers/Gothenburg
  • Apr 24-28, 2023: Arithmetic Statistics, Automorphic Forms and Ergodic Methods, MPIM Bonn
  • May 7-13, 2023: Group actions and harmonic analysis in number theory, MFO
  • May 30, 2023: Number theory seminar, Shandong University (online)
  • Jun 12-16, 2023: (minicourse) Geometry and spectra of random hyperbolic surfaces, Université de Montréal
  • Sep 11-16, 2023: (organizer) Groups and rigidity around the Zimmer program, Ventotene
  • Oct 4-6, 2023: Women in automorphic forms, Konstanz

  • Miscellanea

  • Minicourse notes (counting/equidistribution/spectral gap) - Ventotene Conference on Counting Problems (2021)
  • Spectral theory of hyperbolic surfaces - Lecture notes, ETH (2021)
  • Archive (2018-19) of the Number Theory Seminar at Rutgers: Fall 19, Spring 19, Fall 18, Spring 18
  • Combinatorics - weeklong course prepared for the DIMACS RYSP summer program (2019)
  • Theory of Numbers - Lecture notes for Math 356, Rutgers (2019), see also the course syllabus
  • Geometry - Lecture notes for Math 435, Rutgers (2017)
  • A dynamical outlook on orbital counting problems (with Xin Zhang) (2014)
  • Quasihomomorphisms and refinements of property (T) - Master thesis, ETH Zürich, 2012
  • Autour du théorème de Szemerédi - EA, École Polytechnique (2010)
  • Uniquely ergodic rotations, nilrotations, and equidistribution - Bachelor thesis, ETH (2010)

  • Zurich, January 2023