Ian Biringer
Assistant Professor

Department of Mathematics
Boston College

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

CV


Research


Most of my work is inspired or influenced by hyperbolic geometry. I am also interested in combinatorial and geometric group theory, differential geometry and the geometry of lattices in higher rank Lie groups.

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

Teaching


I am a strong proponent of introducing inquiry based learning (IBL) methods into undergraduate education, whether by teaching non-lecture-based courses or by introducing some discovery and experimentation based activities into lecture courses. A fascinating study on the effectivity of IBL can be found here.

This semester at BC, I am teaching MT 451.

Papers


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. (to appear in Journal of Topology)

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

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

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