City University of New York, Graduate Center and Hunter College, Mathematics Department, Professor.
Ph.D. in Mathematics from Stony Brook University.
The study of geometric structures on manifolds.
Education and Academic Employment
|Ph.D., State University of New York, Stony Brook; December 1987; Dissertation Advisor Professor Bernard Maskit|
|M.A., State University of New York, Stony Brook, August 1983|
|B.A., Queens College, City University of New York, May 1981|
|Professor, Graduate Center and Hunter College, City University of New York 2006-present. Graduate Center appointment, 2007-present.|
|Professor, University of Oklahoma, Norman, ; 1999-2006|
|Associate Professor, University of Oklahoma, Norman, ; 1994-1999|
|Assistant Professor, University of Oklahoma, Norman, ; 1988-1994|
|Assistant Professor, Fordham University, Bronx, NY 10458, 1987-1988|
Research Fields of Interest
- Hyperbolic geometry, Riemann surfaces, geometric structures on manifolds.
- Constructing Pairs of Pants”, Ann. Acad. Sci. Fennicae, Series A. I. Math. 15, 1990, 65-74.
- Generalizing the hyperbolic collar lemma”, Bulletin of the Amer. Math. Soc., 27, 1, July 1992, 154-158.
- Hyperbolic structures for surfaces of infinite type”, Transactions of the Amer. Math. Soc. 336, no. 1, March 1993, 421-444.
- The geometry of totally geodesic hypersurfaces in hyperbolic manifolds”, Differential geometry: Riemannian geometry (Los Angeles, CA, 1990), 81–87, Proc. Sympos. Pure Math., 54, Part 3, Amer. Math. Soc., Providence, RI, 1993.
- The stable neighborhood theorem and lengths of closed geodesics”, Proc. of the Amer. Math. Soc., 119, 1, Sept. 1993, 217-224.
- The orthogonal spectrum of a hyperbolic manifold”, American Journal of Mathematics, 115, 5, Oct. 1993, 1139-1159.
- Tubular neighborhoods of totally geodesic hypersurfaces in hyperbolic manifolds”, Inventiones Mathematicae, 117, 1994, 207-225.
- Constructing pairs of pants II”, Low-dimensional topology (Knoxville, TN, 1992), 15-20, Conf. Proc. Lecture Notes Geom. Topology, III, Internat. Press, Cambridge, MA, 1994.
- Metric flows in space forms of nonpositive curvature”, Proc. of the Amer. Math. Soc., 123, 10, Oct. 1995, 3177-3181. (With Gerard Walschap)
- Selected problems in Kleinian groups and hyperbolic geometry”, Lipa’s legacy (New York, 1995), 9-15, Contemp. Math., 211, Amer. Math. Soc., Providence, RI, 1997.
- Large parameter spaces of quasiconformally distinct hyperbolic structures”, Journal D’Analyse Mathematique, 71, 1997.
- Discrete subgroups of complex hyperbolic motions”, Inventiones Mathematicae, 131, 1998, 85-136. (with Robert Miner)
- Quasiconformal mappings and geodesics in the hyperbolic plane”, In the tradition of Ahlfors and Bers (Stony Brook, NY, 1998), 1–4, Contemp. Math., 256, Amer. Math. Soc., Providence, RI, 2000.
- Hyperbolic 3-manifolds with nonintersecting closed geodesics”, Geometriae Dedicata, 97 (2003), 251-257. (with Scott Wolpert)
- The Mobius transformations of the circle form a maximal convergence group”, The geometry of Riemann surfaces and abelian varieties, III Iberoamerican Congress on Geometry, Contemp. Math., 397, Amer. Math. Soc., Providence, RI, 2006. (with Mahmoud Zeinalian)
- Maximal convergence groups and rank one symmetric spaces”, Journal of the Australian Mathematical Society, 83 (1), August 2007. (with Mahmoud Zeinalian)
- Geometrically infinite surfaces with discrete length spectra”, Geometriae Dedicata, 137 (2008), 219-240. (with Youngju Kim)
- Space form isometries as commutators and products of involutions”, Trans. Amer. Math. Soc. 364 (2012), no. 9, 5015–5033. (with Bernard Maskit).
- Generating the Mobius group with involution conjugacy classes”, Proc. Amer. Math. Soc. 140 (2012), no. 11, 4011–4016. (with Karan Puri).
- Conformally scattered sets in the unit circle”, Quasiconformal mappings, Riemann surfaces, and Teichmuller spaces, 23–29, Contemp. Math., 575, Amer. Math. Soc., Providence, RI, 2012.
- Universal length bounds for non-simple closed geodesics on hyperbolic surfaces”, submitted.
|Mathematics Graduate Student Organization outstanding faculty teaching award, University of Oklahoma, 1997, 2003.ト|
|Harry S. Kieval Lecturer, Southern Oregon State College, Ashland, Oregon, 1996-97.|
|National Science Foundation Research Grant DMS- 9404174 awarded for July 1, 1994 to December 31, 1997, (with Robert Miner).|
|National Science Foundation Grant for Computing equipment involving graphics visualization, DMS-9405158, (with Robert Miner).|
|Selected to serve on the 56th College of National Lecturers for Sigma Xi (an honorary society for scientists and engineers) from July 1, 1995 to June 30, 1997.|
|American Mathematical Society/National Science Foundation Travel Grant for the International Congress of Mathematicians, August, 1994.|
|National Science Foundation Grant DMS-9400754, 1994, Research Experiences for Undergraduates.|
|University of Oklahoma College of Arts and Sciences Junior Faculty Summer Fellowship, 1993.|
|National Science Foundation Travel Grant DMS-9207019, 1992-94.|
|National Science Foundation Grant DMS-9000624, 1990, Research Experiences for Undergraduates project.|
|President’s Award for Excellence in Teaching by a Graduate Student, SUNY, Stony Brook, 1985.|
Running, cycling (spin instructor), triathlon, baseball.