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, automorphic forms, and spectral methods. Before joining UZH, I was a senior research associate at ETH (Oberassistentin) and a Hill assistant professor at Rutgers University.


Teaching
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: Lfunctions and modular forms
Beware: These notes have not been revised  they will contain typos

Publications, preprints, and work in preparation
On the nonmultiplicativity of Fourier coefficients of cusp forms. In preparation.
Rational points on spheres, with Matthias Gröbner. In preparation (2023).
Pairs in discrete lattice orbits with applications to Veech surfaces,
with Samantha Fairchild and an appendix by Jon Chaika. Submitted (2022).
Windings of prime geodesics, with Flemming von Essen. Submitted (2023).
The ManinDrinfeld theorem and the rationality of Rademacher symbols.
Journal de Théorie des Nombres de Bordeaux 34 (3) (2022), 739753.
Translates of rational points on expanding horocycles on the modular surface,
with Uri Shapira, 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.
Conferences and seminars
I am part of the Zurich Dynamics and Ergodic Theory group and a coorganizer of the joint Ergodic Theory and Dynamical Systems Seminar between ETH and UZH.

This year I am also coorganizing with Yingkun Li, Christina Roehrig and Riccardo Zuffetti the online international seminar on automorphic form, taking place Tuesdays 1617h (CET). Website here!

Alessandra Iozzi, Michah Sageev and I are organizing the next edition of Ventotene on Groups and Rigidity in the Zimmer Program (GRAZP), September 1116 2023

Corinna Ulcigrai and I just organized this year's Swiss Mathematical Society autumn conference on Dynamics and Groups at UZH, September 1416, 2022
Recent & upcoming talks
Nov 2325, 2022: Stochastic geometry workshop, Osnabrück
Dec 89, 2022: Crosscurrents in number theory, analysis and geometry, Paris 13
Feb 23, 2023: Number theory seminar, Basel
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 2428, 2023: Arithmetic Statistics, Automorphic Forms and Ergodic Methods, MPIM Bonn
May 713, 2023: Group actions and harmonic analysis in number theory, MFO
May 30, 2023: Number theory seminar, Shandong University (online)
Jun 1216, 2023: (minicourse) Geometry and spectra of random hyperbolic surfaces, Université de Montréal
Sep 1116, 2023: (organizer) Groups and rigidity around the Zimmer program, Ventotene
Oct 46, 2023: Women in automorphic forms, Konstanz


Miscellanea
Minicourse notes (counting/equidistribution/spectral gap)  Ventotene Conference on Counting Problems (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, January 2023
