Claire Burrin


Hill Assistant Professor
Department of Mathematics
Rutgers University  Hill Center
110 Frelinghuysen Rd
Piscataway, NJ 088548019
Office: Room 232, Hill Center
EMail: claire.burrin@rutgers.edu



Using ideas from analytic number theory, harmonic analysis, automorphic forms, and homogeneous dynamics, I study problems relating the arithmetic and geometry of discrete subgroups of Lie groups.

Teaching  Spring 2020
Math 350H Honors Linear Algebra  Syllabus

Math 477 Probability Theory  Syllabus

Research projects  If you are a math major interested in working on a research project, you can contact me!

Recent Talks
Jan 1: Weizmann Institute, Midrasha on Groups

Jan 2: Technion, Groups, Dynamics, and Related Topics Seminar

Jan 30: QuébecVermont Number Theory Seminar, Montréal

Publications, preprints, and work in preparation

Translates of rational points on expanding horocycles on the modular surface,
with Uri Shapira and Shucheng Yu. In preparation.

The SiegelVeech transform for pairs and applications.
with Samantha Fairchild. In preparation.

Windings of prime geodesics,
with Flemming von Essen. In preparation

Effective counting for discrete lattice orbits in the plane via Eisenstein series,
with Amos Nevo, Rene Rühr, Barak Weiss. Preprint (2019).

Transformation laws for generalized Dedekind sums associated to Fuchsian groups,
with Jay Jorgenson, Cormac O'Sullivan, Lejla Smajlović.
To appear in Acta Arithmetica.

Dedekind sums, reciprocity, and nonarithmetic groups.
Contemporary Mathematics 732 (2019), pp. 1925.

Reciprocity of Dedekind sums and the Euler class.
Proc. Amer. Math. Soc. 146 (2018), pp. 13671376.

Generalized Dedekind sums and equidistribution mod 1.
Journal of Number Theory 172 (2017), pp. 270286.

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


Short CV (pdf)
Fall 2020: CRMISM Postdoctoral Fellow, Université de Montréal.

20162020: Hill Assistant Professor, Rutgers University.

20122016: PhD, ETH Zurich. Program Associate, MSRI (2015). Visiting student, Princeton University (2013).

20072012: BSc, MSc in Mathematics, ETH Zurich. M1 at École Polytechnique (20102011).


Miscellanea
From September 2017 to December 2019, I organized the Number Theory Seminar at Rutgers.
Here is the archive:
Fall 2019,
Spring 2019,
Fall 2018,
Spring 2018
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)
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 June 2019
