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College of Arts and Sciences

Martin Bridgeman

department of mathematics


Associate Professor

Ph.D. Princeton University

361 Carney Hall
617-552-3770
Email: bridgem@bc.edu
Webpage: http://www2.bc.edu/~bridgem/

Research...

Professional History

My main areas of research are Hyperbolic geometry, Kleinian groups and Teichm├╝ller theory. One interest is the relation between the convex hull of a Kleinian group and its conformal structure at infinity. Another is the interplay between the conformal dynamics and Kleinian groups via Patteron-Sullivan theory and geodesic currents, in order to develop structures and invariants for hyperbolic spaces and their moduli spaces. One such structure of interest is to extend the classical Weil-Petersson metric on Teichm├╝ller space to other moduli spaces such as Quasifuchsian space and Schottky space.

Selected Publications

  • An extension of the Weil-Petersson metric to quasi-fuchsian space, (with Edward Taylor), Mathematische Annalen 341, No. 4 (2008).
  • Distribution of intersection lengths of a random geodesic with a geodesic lamination, (with David Dumas), Ergodic Theory and Dynamical Systems 27, No. 4 (2007).
  • Patterson-Sullivan measures and quasi-conformal deformations, (with Edward Taylor), Communications in Analysis and Geometry 13, No. 3 (2005).
  • Bounding the bending of a hyperbolic three-manifold, (with Richard Canary), Pacific Journal of Mathematics 218, No. 2 (2005).
  • From the boundary of the convex core to the conformal boundary, (with Richard Canary), Geometrica Dedicata 96, No. 1 (2003).
  • Length distortion and the Hausdorff dimension of limit sets, (with Edward Taylor), American Journal of Mathematics 122 (2000).

Average bending of convex pleated planes in H3, Inventiones Mathematicae 132 (1998).

Current Courses