Claire Burrin

Hill Assistant Professor
Department of Mathematics
Rutgers University - Hill Center
110 Frelinghuysen Rd
Piscataway, NJ 08854-8019

Office: Room 232, Hill Center
E-Mail: claire.burrin@rutgers.edu

I am a Hill Assistant Professor at Rutgers University. My mentors are Henryk Iwaniec and Alex Kontorovich. I study number-theoretical aspects of discrete subgroups of SL(2,R) and PSL(2,R), and its interactions with homogeneous dynamics, hyperbolic geometry, spectral geometry, and the theory of automorphic forms. Before coming to Rutgers, I received my PhD in June 2016 from ETH Zürich, where my advisor was Alessandra Iozzi.

Short CV
Rutgers' Number Theory Seminar - Fall 2019
Math 477 Probability Theory - Syllabus
Research projects - If you are a math major interested in working on a research project, you can contact me!

Upcoming talks

Sep 4: UC Berkeley, Topology Seminar
Oct 5-6: Maine-Québec Number Theory Conference
Oct 15: Rutgers, Geometry/Topology Seminar
Nov 13: Boston College, Dynamics Seminar
Nov 21: Joint NY-CUNY-Columbia Number Theory Seminar

Publications and preprints

  1. Windings of prime geodesics [Available upon request]
    With Flemming von Essen

  2. Effective counting for discrete lattice orbits in the plane via Eisenstein series [ArXiv:1905.01493]
    With Amos Nevo, Rene Rühr, Barak Weiss
  3. Transformation laws for generalized Dedekind sums associated to Fuchsian groups [ArXiv:1904.11333]
    With Jay Jorgenson, Cormac O'Sullivan, Lejla Smajlović

  4. Dedekind sums, reciprocity, and non-arithmetic groups [ArXiv:1809.03038] [Contemp. Math.]
    Contemporary Mathematics 732 (2019), pp. 19-25

  5. Reciprocity of Dedekind sums and the Euler class [ArXiv:1609.03588] [Proc. AMS]
    Proc. Amer. Math. Soc. 146 (2018), pp. 1367-1376

  6. Generalized Dedekind sums and equidistribution mod 1 [ArXiv:1509.04429] [J. Number Theory]
    Journal of Number Theory 172 (2017), pp. 270-286


Theses

  1. Dedekind symbols and applications of the spectral theory of Kloosterman sums
    Dissertation ETH No. 23634, 2016 (awarded ETH medal and money-prize)

  2. Quasihomomorphisms and refinements of property (T)
    Master thesis, ETH Zürich, 2012


Miscellanea

  • 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)
  • Autour du théorème de Szemerédi - EA, École Polytechnique (2010)
  • Uniquely ergodic rotations, nilrotations, and equidistribution - Bachelor thesis, ETH (2010)
  • Rutgers' Number Theory Seminar archive: Spring 2019, Fall 2018, Spring 2018
  • Some older teaching at ETH: Multilinear algebra (Spring 2016), Modular forms (Fall 2015), Mathematics (Fall 2014), Algebra 2 (Spring 2014), Algebra 1 (Fall 2013)


  • Last updated in Aug 2019