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: Lfunctions 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 1517: goMath minisymposium: 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 27Jul 1: Marc Burger's Prime, ETH Zurich
Aug 2226: Modular forms in number theory and beyond, Universität Bielefeld
Oct 25: Charles University Prague, Number Theory Seminar
Nov 2325: Stochastic geometry workshop, Universität Osnabrück
Apr 2428: 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 SiegelVeech 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 ManinDrinfeld 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), 655717.
Infinitely many twin prime polynomials of odd degree, with Matthew Isaac.
The American Mathematical Monthly 128 (2021), no. 10, 929935.
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. 34, 259304.
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 nonarithmetic 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 (201819) 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
