Areas of Expertise
Differential geometry, generic geometry through singularity theory
- May 1998: Ph.D. Mathematics Brown University
- May 1995: Sc.M. Mathematics Brown University
- May 1993: B.A. Mathematics, High Distinction, University of Virginia
- 2017: Sigma Alpha Pi Teacher of the Year
- 2007: 2007 Outstanding Undergraduate Teaching Award, University of North Florida
- 2003: UNF Student's Choice Award, Mathematics
- 2003: Award for Innovative Excellence in Teaching, Learning and Technology, The 14th International Conference on College Teaching and Learning
- 2002: 2002 Outstanding Undergraduate Teaching Award, University of North Florida
- 1999-2000: Project NExT Fellow
- 1998: Outstanding Teaching Prize in Mathematics, Brown University.
Grants and Contracts Awarded
- Summer 2009: Teaching Grant, Awarded by University of North Florida, "Undergraduate Elliptic Curves"
- Summer 2007: Research Grant, Awarded by University of North Florida, "4-D Geometry of Lighted Surfaces"
- Summer 2002: Teaching Grant, Awarded by University of North Florida, "Using the web in Explorations".
- Summer 2001: Teaching Grant, Awarded by University of North Florida, "Improving the computer-based college algebra system".
- Summer 2000: Research Grant, Awarded by University of North Florida, "Parabolic curves of evolving surfaces in R4.
- Summer 1999: Technology and Teaching Grant, Awarded by University of North Florida, "Using WebCT in Explorations of Mathematics".
- Summer 1998: Communications in Visual Mathematics, Awarded by the Mathematical Association of America.
- Summer 1992: Research Experiences for Undergraduates, Awarded by the National Science Foundation.
Publications & Presentations
- “Gauss maps and duality of sphere bundles”, Real and Complex Singularities, Contemp. Math., Math. Soc., 2016.
- With R. Araújo dos Santos. N. Dutertre, "Topology of the real Milnor fiber for isolated singularities", Real and complex singularities, 67–75, Math., 569, Amer. Math. Soc., Providence, RI, 2012.
- "Self-conjugate Vectors of Immersed 3-manifolds in R6", Topology and its Applications, 159 (2012), no. 2, 450-456.
- "Conjugate Vectors of Immersed Manifolds," Real and Complex Singularities, 1-12, Contemp. Math., 459, Math. Soc., 2008.
- "The Geometry of Flecnodal Pairs," Real and Complex Singularities, Trends in Mathematics (2007), 113-126.
- "Birth of bitangencies in a family of surfaces in R4," Differential Geometry and its Applications. 24 (2006), no. 4, 321-331.
- "Invariance of the Diagonal Contribution in a Bitangency Formula," Real and Complex Singularities, 45-56, Contemp. Math., 354, Math. Soc., 2004.
- "Singularities of the Gauss Map and Binormal Surfaces," Advances in Geometry, 3 (2003), 453-468.
- "A Self-Intersecting Sphere," EG-Models, 2002.
- "A Bitangency Theorem for Surfaces in Four-Dimensional Euclidean Space," Quarterly Journal of Mathematics, 52 (2001).
- Editor for web version: T. Banchoff, T. Gaffney, and C. McCrory, "Cusps of Gauss Mappings," web version, Electronic Library of Mathematics, European Mathematical Information Service. 1998.
- "A Bitangency Theorem for Immersed Surfaces in Four-Dimensional Euclidean Space," Ph.D. dissertation.
- With J. Rovnyak and K. Y. Li, "Coefficients of Bounded Univalent Functions," Proceedings of the Conference of Complex Analysis (Tianjin, 1992), 45-48, Conference Proceedings and Lecture Notes in Analysis.