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

Conference: Dynamics and Groups

Corinna Ulcigrai and I are organizing this year's Swiss Mathematical Society autumn conference on Dynamics and Groups. Speakers and registration are here.

International Seminar on Automorphic Forms

This year, I am organizing with Yingkun Li and Riccardo Zuffetti the online international seminar on automorphic forms. More to come soon!

Teaching

Fall 2022: CUSO Graduate Lectures, Spectral theory of hyperbolic surfaces
Spring 2022: Topics in number theory: L-functions and modular forms
Lecture Notes (updated June '22) (Caveat: these notes have not been revised - they will contain typos)

Recent & upcoming talks

Feb 14: Jacobs University Bremen, Online dynamics seminar
Feb 28: University of Hong Kong, Number Theory Seminar
Mar 15-17: goMath mini-symposium: Harmonic Analysis and Number Theory, ETH Zurich
Apr 4: EPFL, Groups, arithmetic, and algebraic geometry seminar
Apr 11: ETH/UZH, Ergodic theory and dynamics seminar
May 3: Université de Fribourg, Colloquium
Jun 27-Jul 1: Marc Burger's Prime, ETH Zurich
Aug 22-26: Modular forms in number theory and beyond, Universität Bielefeld
Oct 25: Charles University Prague, Number Theory Seminar
Nov 23-25: Stochastic geometry workshop, Universität Osnabrück
Apr 24-28: Conference on "Arithmetic Statistics, Automorphic Forms and Ergodic Methods", MPIM Bonn

Publications, preprints, and work in preparation

  • On the nonmultiplicativity of Fourier coefficients of cusp forms. In preparation.
  • The Siegel-Veech transform for pairs of discrete lattice orbits in the plane, with Samantha Fairchild and an appendix by Jon Chaika. Preprint (2022).
  • Windings of prime geodesics, with Flemming von Essen. ArXiv preprint (2022).
  • The Manin-Drinfeld theorem and the rationality of Rademacher symbols.
  • Journal de Théorie des Nombres de Bordeaux 34 (3) (2022).
  • Translates of rational points on expanding horocycles on the modular surface, with Uri Shapira and 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

  • Minicourse notes (counting/equidistribution/spectral gap) - Ventotene Conference (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, June 2022