Claire Burrin


ETH Zürich
Department of Mathematics
Rämistrasse 101
8092 Zürich, Switzerland
Office: HG G66.4
Phone: +41 44 632 8910
claire.burrin@math.ethz.ch



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

Starting February 1, 2022, I will be assistant professor (SNSF PRIMA Professor) at the University of Zurich.

Teaching
Spring 2022: Topics in number theory: Lfunctions and modular forms (UZH)
Spring 2021: Spectral theory of hyperbolic surfaces (ETH)

Recent & upcoming talks
Fall 2021
Aug 18: MPIM Bonn, Number Theory Lunch Seminar
Sep 611: Minicourse speaker, Ventotene international workshop on counting problems, Ventotene, Italy
Oct 19: University of Exeter, Dynamics Seminar
Nov 9: Special year on triangle groups, Belyi uniformization, and modularity, Bhaskaracharya Pratishan
Dec 14: Université de Fribourg, Colloquium (postponed to 2022)
Dec 16: Séminaire virtuel francophone Groupes et Géométrie

2022
Jun 27Jul 1: Marc Burger's Prime, ETH Zurich
Aug 2226: Modular forms in number theory and beyond, Universität Bielefeld

Publications, preprints, and work in preparation
The SiegelVeech 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 ManinDrinfeld theorem and the rationality of Rademacher symbols. Accepted for publication in Journal de Théorie des Nombres de Bordeaux (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. 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.
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
Minicourse notes (counting/equidistribution/spectral gap)  Ventotene Conference (2021)
Spectral theory of hyperbolic surfaces  Lecture notes for course taught at 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, November 2021
