## Areas of Expertise

Differential geometry, generic geometry through singularity theory

## Education

**May 1998:**Ph.D. Mathematics Brown University**May 1995:**Sc.M. Mathematics Brown University**May 1993:**B.A. Mathematics, High Distinction, University of Virginia

## Biography

## Awards

**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**R**^{4}.**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
**R**^{6}",*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
**R**^{4},"*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.

Contact Information

(904) 620-3718