Ian Biringer Gibbs Assistant Professor Department of Mathematics Yale University Email: ian.biringer@yale.edu Office: DL 421 CV

Research Most of my work is inspired or influenced by hyperbolic geometry, although I am also interested in combinatorial and geometric group theory, differential geometry and the geometry of lattices in higher rank Lie groups. I coorganize the Yale geometry/topology seminar. 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. 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. (submitted) Intersection growth in groups. Joint with Khalid Bou-Rabee, Martin Kassabov and Francesco Mattucci. (in preparation) On the growth of L2-invariants for lattices in Lie groups. Joint with M. Abert, N. Bergeron, T. Gelander, N. Nikolov, J. Raimbault and I. Samet. (in preparation) A research announcement is available on the Arxiv Rank and topology of hyperbolic 3-manifolds. Joint with Juan Souto. (in preparation)