Ian Biringer
Assistant Professor

Department of Mathematics
Boston College

Email: ian.biringer@bc.edu
Office: Carney 315



Most of my work is inspired or influenced by hyperbolic geometry.

I co-organize the Geometry/Topology seminar at BC. A schedule can be found here.


This semester I am teaching Multivariable Calculus. The course webpage is here.

A set of notes on Euclidean and Non-Euclidean geometry that I wrote that are suitable for students with only a multivariable calculus background are available here.


Algebra vs. geometry in hyperbolic 3-manifolds. pdf
PhD thesis, University of Chicago.

The Three Gap Theorem and Riemannian Geometry. Arxiv
Joint with Benjamin Schmidt. Geometriae Dedicata, vol. 136 (2008).

Geometry and Rank of Fibered Hyperbolic 3-Manifolds. Arxiv
Algebr. Geom. Topol. 9 (2009).

Algebraic and Geometric Convergence of Discrete Representations into PSL(2,C). Arxiv
Joint with Juan Souto. Geometry and Topology 14 (2010).

A finiteness theorem for closed hyperbolic 3-manifolds. Arxiv
Joint with Juan Souto. Journal of the London mathematical society (2011).

Extending pseudo-Anosov maps to compression bodies. Arxiv
Joint with Yair Minsky, Jesse Johnson. Journal of Topology (2013).

On the growth of L2-invariants for sequences of lattices in Lie groups. Arxiv
Joint with M. Abert, N. Bergeron, T. Gelander, N. Nikolov, J. Raimbault and I. Samet.
A research announcement is available here.

Intersection growth in groups. Arxiv
Joint with Khalid Bou-Rabee, Martin Kassabov and Francesco Mattucci.

Unimodularity of invariant random subgroups. Arxiv
Joint with Omer Tamuz.

Automorphisms of the compression body graph. Arxiv
Joint with Nicholas Vlamis.

The topology of invariant random surfaces. Arxiv
Joint with Jean Raimbault.

Rank of mapping tori via the curve complex. Arxiv
Joint with Juan Souto.

Rank and topology of hyperbolic 3-manifolds.
Joint with Juan Souto. (in preparation)

Invariant measures on the space of all Riemannian manifolds.
Joint with Miklos Abert. (in preparation)