Sde-Boker lecture (photo by T. Gelander)
Welcome to the math homepage of

Peter Storm

Research Interests

I am interested in geometry and topology. Specifically, my research studied hyperbolic geometry and related topics. My thesis advisor was Richard Canary .

Personal History:

  • University of Pennsylvania, Assistant Professor, 2007-2009
  • Stanford University, Szegő Assistant Professor, 2004-2007
  • University of Chicago, L.E. Dickson Instructor, 2003-2004
  • University of Michigan, Ph.D. in mathematics, 1998-2003
  • University of Chicago, B.A. in mathematics, 1994-1998
    Papers and preprints: (Please follow the "journal version" link for published papers. Most of these papers are also available on ArXiv.)

    (18) "Lipschitz minimality of Hopf fibrations and Hopf vector fields", with Dennis DeTurck and Herman Gluck, Algebraic and Geometric Topology 13 (2013) 1369-1412.

    (17) "Hyperbolic 3-manifolds", with Robert Meyerhoff, McGraw Hill 2010 Yearbook of Science & Technology.

    (16) "Moduli spaces of hyperbolic 3-manifolds", with Richard Canary, Commentarii Mathematici Helvetici 88 Issue 1 (2013) 221-251.

    (15) "The curious moduli space of unmarked Kleinian surface groups", with Richard Canary, The American Journal of Mathematics 134 Number 1, 71-85.

    (14) "Local rigidity of hyperbolic manifolds with geodesic boundary", with Steven Kerckhoff, Journal of Topology 5 Issue 4, 757-784

    (13) "Infinitesimal rigidity of a compact hyperbolic 4-orbifold with totally geodesic boundary", with Tarik Aougab, Algebraic & Geometric Topology 9 (2009) 537-548. We prepared notebooks to explain the computations of this paper in detail. This article was the result of an NSF-supported undergraduate research project with Tarik in the summer of 2008.

    (12) "From the 24-cell to the cuboctahedron", with Steven Kerckhoff, Geometry & Topology 14 (2010) 1383-1477. This article uses lots of color.

    (11) "Finiteness of arithmetic hyperbolic reflection groups", with Ian Agol, Mikhail Belolipetsky, and Kevin Whyte, Groups, Geometry, and Dynamics2 Issue 4 (2008) 481-498

    (10) "Dense embeddings of surface groups", with Emmanuel Breuillard, Tsachik Gelander, and Juan Souto, Geometry & Topology 10 (2006) 1373-1389

    (9) "Lower bounds on volumes of hyperbolic Haken 3-manifolds", with Ian Agol and Bill Thurston, and an appendix by Nathan Dunfield, Journal of the American Mathematical Society 20 (2007) 1053-1077

    (8) "The Novikov conjecture for mapping class groups as a corollary of Hamenstadt's theorem"

    (7) "Finitely generated subgroups of lattices in PSL(2,C)", with Yair Glasner and Juan Souto, Proceedings of the American Mathematical Society 138 (2010) 2667-2676.

    (6) "Dynamics of the mapping class group action on the variety of Sl(2,C)-characters", with Juan Souto, Geometry & Topology 10 (2006) 715-736

    (5) "Rigidity of minimal volume Alexandrov spaces", Annales Academiæ Scientiarum Fennicæ Mathematica 31 (2006) 381-389

    (4) "Hyperbolic convex cores and simplicial volume", Duke Mathematical Journal 140 No.2 (2007) 281-319

    (3) "The minimal entropy conjecture for nonuniform rank one lattices", Geometric and Functional Analysis 16 No.4 (2006) 959-980

    (2) "The barycenter method on singular spaces", Commentarii Mathematici Helvetici 82 Issue 1 (2007) 133-173

    (1) "Minimal volume Alexandrov spaces", Journal of Differential Geometry 61 (2002) 195-226

    During the spring of 2009 I taught a course on mapping class groups at Hebrew University in Jerusalem.
    Scanned notes are available. View the homepage.
    View my gallery of computer images. (It may load slowly.)
    I wrote pinlabeler, a graphical extension to Colin Rourke's excellent figure labelling tex package pinlabel. With your latex file open in a text editor, pinlabeler opens a gv window showing your figure. Rather than manually copying coordinates from gv to your latex file, left-clicking in pinlabeler's gv window sends the coordinates to the latex file automatically. The coordinates are formatted for pinlabel.

    Nathan Dunfield has written a very similar (and probably better) program labelpin. It works on Macs.

    More information about pinlabeler.

    Time to kill? Try the take-home final exam I prepared for undergraduate honors algebra at the University of Chicago in 2004, or my in-class final exam for undergraduate honors analysis at Stanford in 2007. (Most of the questions are taken from various long-forgotten sources.)
    Many thanks to the University of Pennsylvania for hosting my webpage.