Claire Burrin

ETH Zürich
Department of Mathematics
Rämistrasse 101
8092 Zürich, Switzerland

Office: HG J16.2
Phone: +41 44 632 40 97

I am a Senior Research Associate (Oberassistentin) at ETH Zürich. My research is in number theory, and its connections with geometry and dynamics.

Teaching - Spring 2021

Spectral theory of hyperbolic surfaces

Recent & upcoming talks

  • Apr 7: University of Wisconsin-Madison, Dynamics seminar
  • May 5: University of Bristol, Heilbronn Number Theory Seminar
  • Jun 8: International Seminar on Automorphic Forms
  • Jul 6: Online workshop on Eisenstein series and equivariant cohomology
  • Aug 2: COGENT seminar
  • Aug 18: MPIM Bonn, Number Theory Lunch Seminar
  • Sep 6-11: Mini-course speaker, Ventotene international workshop on counting problems, Ventotene, Italy
  • Oct 19: University of Exeter, Dynamics Seminar
  • Nov 23: Special year on triangle groups, Belyi uniformization, and modularity, Bhaskaracharya Pratishan, Pune, India

  • Publications, preprints, and work in preparation

  • The Siegel-Veech transform for pairs of discrete lattice orbits in the plane, with Samantha Fairchild and an appendix by Jon Chaika. In preparation.
  • Windings of prime geodesics, with Flemming von Essen. Preprint, 2021.
  • The Manin-Drinfeld theorem and the rationality of Rademacher symbols. Submitted, 2021.
  • Translates of rational points on expanding horocycles on the modular surface, with Uri Shapira and Shucheng Yu. Accepted for publication in Mathematische Annalen (2021).
  • Infinitely many twin prime polynomials of odd degree, with Matthew Isaac, 2019. Accepted for publication in the American Mathematical Monthly (2021).
  • Effective counting for discrete lattice orbits in the plane via Eisenstein series, with Amos Nevo, Rene Rühr, Barak Weiss. L'Enseignement Mathématique (2) 66 (2020), 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. Proc. Amer. Math. Soc. 146, no.4, 2018.
  • Generalized Dedekind sums and equidistribution mod 1. J. Number Theory 172, 2017.
  • Dedekind symbols and applications of the spectral theory of Kloosterman sums. Dissertation ETH No. 23634, 2016. Awarded the ETH medal for outstanding thesis.

  • Miscellanea

  • CV
  • 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 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, September 2021