Claire Burrin

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

Office: Y27K26
Tel.: +41 44 635 58 86
claire.burrin@math.uzh.ch

My research explores connections between number theory, geometry and dynamics. I am at the moment in particular interested in counting problems related to spectral geometry and automorphic forms, see here for more. I am part of the Zurich Dynamics and Ergodic Theory group, and of the SwissMAP research network.

Teaching

  • Spring 2024, 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 and preprints

  • On the crossing number of arithmetic curve systems, with Sebastian Baader and Luca Studer, arXiv 2403.05194, submitted.
  • Rational points on ellipsoids and modular forms, with Matthias Gröbner. arXiv 2401.18008, submitted.
  • Pairs in discrete lattice orbits with applications to Veech surfaces, with Samantha Fairchild and an appendix by Jon Chaika. Journal of the European Mathematical Society (JEMS), to appear.
  • Windings of prime geodesics, with Flemming von Essen. arXiv 2209.06233, submitted.
  • 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.

    Miscellanea (not intended for publication)

  • Minicourse notes (counting/equidistribution/spectral gap) - Ventotene Conference on Counting Problems (2021)
  • A dynamical outlook on orbital counting problems (with Xin Zhang) (2014)
  • Quasihomomorphisms and refinements of property (T) - Master thesis, ETH Zürich, 2012

    Conferences and seminars

    I am/was a co-organiser of the following events
  • International Workshop on Automorphic Forms, SwissMAP research station, Les Diablerets, September 2025, with Luis Garcia (UCL), Yingkun Li and Riccardo Zuffetti (TU Darmstadt)
  • Ergodic Theory and Dynamical Systems Seminar between ETH and UZH, with Menny Aka, Artur Avila, Manfred Einsiedler, Alex Gorodnik, Cagri Sert, Corinna Ulcigrai, Hao Wu
  • International Seminar on Automorphic Forms (online), with Luis Garcia (UCL), Yingkun Li and Riccardo Zuffetti (TU Darmstadt)
  • Ventotene Conference on Groups and Rigidity in the Zimmer Program (GRAZP), September 11-16 2023 in Ventotene, Italy
  • Swiss Math Society Fall Conference Dynamics and Groups, September 14-16, 2022, at UZH
  • At Rutgers: Rutgers Number Theory Seminar (with Henryk Iwaniec, Alex Kontorovich, and Steve D. Miller), Postdoc Colloquium (with Amita Malik, Kei Nakamura)

    Recent & upcoming talks

  • 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
  • Jun 5-9, 2023: (minicourse) Elliptics summer school, Physics Department, UZH
  • Jun 12-16, 2023: (minicourse) Geometry and spectra of random hyperbolic surfaces, Université de Montréal
  • Oct 4-6, 2023: Women in automorphic forms, Konstanz
  • Oct 27, 2023: SMS Fall Conference: Swiss Geometry Days, Brig
  • Dec 18, 2023: Inaugural lecture, UZH (online recording)
  • Jan 22, 2024: Séminaire de théorie ergodique de Rennes
  • Feb 9, 2024: Number theory seminar, University of Virginia
  • Mar 11-15, 2024: Workshop Analytic number theory, Mittag-Leffler
  • May 2, 2024: Sphere packings and magical functions, a talk part of the May12 initiative, UZH (slides)
  • May 13-16, 2024: International Conference on L-Functions and Automorphic Forms, Vanderbilt
  • Aug 5-9, 2024: Workshop on Dynamical Systems at ICTP, Trieste
  • Aug 26-30: Workshop on Combinatorial geometry and number theory, EPFL
  • Sep 9-13, 2024: Geometry and analysis of locally symmetric spaces, Paderborn
  • Mar 10-14, 2025: Recent developments around joint equidistribution in number theory and dynamics, Hausdorff Institute, Bonn

  • Short CV

  • Since 2022: Assistant Professor, SNSF PRIMA Professorship, UZH
  • 2020-2022: Senior Research Associate, ETH
  • Summer 2021: Member, HIM, Bonn; Fall 2020: (Virtual) member, CRM, Montréal
  • 2016-2020: Hill Assistant Professor, Rutgers University. Mentors: Henryk Iwaniec, Alex Kontorovich
  • 2012-2016: PhD student, ETH Zurich. Advisor: Alessandra Iozzi.
  • Spring 2015: Program Associate, MSRI. Spring 2013: Visiting graduate researcher, Princeton University


  • Zurich, April 2024