Publications:

1. R. Penner and A. Papadopoulos, "Enumerating pseudo-Anosov conjugacy classes," Pacific Journal of Math 142, 159-173, (1990).

2. R. Penner, "Bounds on least dilatations," Transactions of the American Math Society 113, 443-450, (1991).

3. R. Penner and A. Papadopoulos, "The Weil-Petersson symplectic structure at Thurston's boundary," Transactions of the American Math Society 335, 891-904, (1993).

4. R. Penner, "Weil-Petersson volumes," Journal of Differential Geometry 35, 559-608, (1992).

5. R. Penner and M. Näätänen, "The convex hull construction for compact surfaces and the Dirichlet polygon," Bulletin London Math Society 23, 568-574, (1991).

6. R. Penner and A. Papadopoulos, "La forme symplectique de Weil-Petersson et le bord de Thurston de l'espace de Teichmüller," Comptes Rendus Acad. Sci. Paris 312, S\'erie I, 871-874, (1991).

7. R. Penner, "Universal constructions in Teichmüller theory," Advances in Mathematics 98, 143-215, (1993).

8. R. Penner, "The Poincaré dual of the Weil-Petersson Kähler form," Communications in Analysis and Geometry 1, 43-70, (1993).

9. R. Penner and M.S. Waterman, "Spaces of RNA secondary structures," Advances in Mathematics, 31-49, (1993).

10. R. Penner and R.J. Milgram, "Riemann's moduli space and the symmetric groups," in Mapping Class Groups and Moduli Spaces of Riemann Surfaces, AMS Contemporary Math 150, 247-290, (1993).

11. R. Penner, "An arithmetic problem in surface geometry," in The Moduli Space of Curves,Birkh\"auser, eds. R. Dijgraaf, C. Faber, G. van der Geer, (1995) 427-466.

12. R. Penner, "The universal Ptolemy group and its completions," in Geometric Galois Actions II, eds. L Schneps and P. Lochak, (Cambridge University Press, 1997) 293-312.

13. R. Penner and P. Glezen, "Some harmonic functions in Minkowski space," Proceedings of the American Mathematical Society 125, 1659-1665, (1997).

14. R. Penner, "The geometry of the Gauss product," in 60th Birthday Festschrift for Yuri I. Manin, (Plenum Press, 1997).

15. R. Penner, "The simplicial compactification of Riemann's moduli space," in Proceedings of the 37th Taniguchi Symposium, (World Scientific, 1996), 237-252.

16. R. Penner and F. Malikov, "The Lie algebra of homeomorphisms of the circle," Advances in Mathematics 140 (1999), 282-322.

17. "On the Hilbert, Fourier and wavelet transforms", preprint (2000).

Invited Talks:

1. Speaker at the Nevanlinna Colloquium at Helsinki, Finland (2000)

2. Speaker at the Nevanlinna Colloquium at EPFL Lausanne, Switzerland (1997)

3. Series of Lectures at Inst. Fourier, Grenoble, France (1996)

4. Series of Lectures at Max Planck Inst. für Math, Bonn, Germany (1996)

5. Principal Speaker at the 37th Taniguchi Symposium, Katinkulta, Finland (1995)

6. Principal Speaker at Math Society of Japan Meeting on the Topology of Moduli Space, Kyoto, Japan (1994)

7. Series of Lectures at University of Bern, Switzerland (1993)

8. Principal Speaker at the Program in Mathematics and Molecular Biology Annual Meeting in Santa Fe (1992)

9. Principal Speaker at Mathematical Sciences Research Institute (1991)

10. Principal Speaker at the Stanford Topology Symposium (1991)

11. Series of Institute Lectures at Institut Mittag-Leffler, Stockholm, Sweden (1990)

12. Address to Finnish Mathematical Society at University of Helsinki (1990)

13. Series of Lectures at CEN Saclay, France (1990)

Monographs

1. (with the assistance of J. L. Harer) Combinatorics of Train Tracks, Annals of Mathematical Studies 125, Princeton Univ. Press (1992).

2. Perspectives in Mathematical Physics International Press, edited by R. C. Penner and S. T. Yau (1994).

3. Discrete Mathematics-proof techniques and mathematical structures, World Scientific Publishing Company (1999).

Patents

1. "Methods of Digital Filtering and Multi-Dimensional Data Compression Using The Farey Quadrature and Arithmetic, Fan, and Molecular Wavelets", World Intellectual Property Organization, International Patent Publication Number WO 00/44104 (July 27, 2000).