Robert Penner
Professor
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MAILING ADDRESS:
Denney Research Building, DRB 155
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Los Angeles, California 90089-1113
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PHONE:
(213) 740-2422
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FAX:
(213) 740-2424
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OFFICE:
DRB 296
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EMAIL:
rpenner@math.usc.edu
Research Interests:
My early research interests were in the fields of low-dimensional
topology and dynamical systems. My doctoral thesis solved an old problem of
Max Dehn and led to a monograph describing the basic theory of train tracks in
surfaces. Turning more towards geometry, I discovered and developed the
decorated Teichmueller theory of punctured surfaces in a series of papers.
I and other researchers have subsequently applied these techinques to various
problems both in mathematics and in the string theory of high-energy physics.
My current research interests include further development of these interfaces
between geometry and physics.
Education:
- B.A. cum laude in Mathematics and with distinction in all subjects from
Cornell University, June 1977
- Ph.D. in Mathematics from Massachusetts Institute of Technology, June l982,
Thesis Advisor: James R. Munkres
- Postdoc at Princeton University, 1982-83 and 84-85,
Supervisor: William P. Thurston
- Postdoc at Institut Mittag-Leffler (Stockholm), 1983-84
Selected Visiting Positions:
Aarhus University, Fall 2006 and 2007-2008; University of Chicago
April/May 2007; Max Planck Inst fur Math (Bonn, Germany) May/June 1996,
June 2005, Feb/Mar 2007; Fields Institute Sept-Nov 2004; Inst Fourier
(Grenoble, France) June 1996; Inst Non-Lineaire de Nice (Nice, France)
Fall 1994 (CNRS Poste Rouge) and July 1996; Inst des Hautes Etudes
Scientifique (Paris, France) Spring 1993 and May 1995, 1996; Stanford
Univ May 1990 and Spring 1986; Univ Louis Pasteur (Strasbourg, France)
Spring 1990 and 1986; Inst Mittag-Leffler (Stockholm, Sweden) Winter
1990; Harvard Univ Fall 1989; Eidgenossiche Technische Hochschule
(Zurich, Switzerland) June 1986 and March 1990; Univ of Warwick
(Coventry, England) April 1986 and 1984.
Monographs:
- 1. (with the assistance of J. L. Harer) Combinatorics of Train Tracks,
Annals of Mathematical Studies, 125, Princeton Univ. Press (1992), 216 pages.
- 2. A Course of Discrete Mathematics, a textbook
submitted for publication (1996), 450 pages.
Selection of Papers:
- 1. ``The action of the mapping class group on curves in surfaces",
L'Enseignement Mathematique, 30 (1984), 39-55.
- 2. ``The decorated Teichmueller space of punctured surfaces",
Communications in Mathematical Physics, 113 (1987), 299-339.
- 3. (with D. B. A. Epstein) Euclidean decompositions of non-compact
hyperbolic manifolds", Journal of Differential Geometry, 27 (1988), 67-80.
- 4. ``Perturbative series and the moduli space of Riemann surfaces",
Journal of Differential Geometry, 27 (1988), 35-53.
- 5. (with A. Papadopoulos) ``La forme symplectique de Weil-Petersson
et le bord de Thurston de l'espace de Teichmueller'', Comptes
Rendus Acad. Sci. Paris, 312 (1991), 871-874.
- 6. ``Weil-Petersson volumes'', Journal of Differential Geometry, 35
(1992), 559-608.
- 7. ``Universal constructions in Teichmueller theory", Advances in
Mathematics, 98 (1993), 143-215.
- 8. (with M. S. Waterman) ``Spaces of RNA secondary structures'' Advances
in Mathematics, 101 (1993), 31-49.
- 9. ``The simplicial compactification of Riemann's moduli space'',
Proceedings of the 37th Taniguchi Symposium, World Scientific (1996).
- 10.
``On the Hilbert, Fourier, and wavelet transforms'',
Communications on Pure and Applied Mathematics 55 (2002),
772-814.