Department of Mathematics and Statistics

University of North Florida

4567 St. John's Bluff Rd., South

Jacksonville, FL 32224

(904) 620-3718

Email: ddreibel@unf.edu

**CURRENT POSITION**

**2004 - Present: **Associate Professor, Department of
Mathematics, University of North Florida

**1998 - Present:** Assistant Professor, Department of Mathematics,
University of North Florida

EDUCATION

**May 1998:** Ph.D. Mathematics Brown University, Providence, RI

**May 1995:** Sc.M. Mathematics Brown University, Providence, RI

**May 1993:** B.A. Mathematics, High Distinction, University of
Virginia, Charlottesville, VA

RESEARCH INTERESTS:

Differential geometry through singularity theory, surfaces immersed in
four-dimensional Euclidean space

**PUBLICATIONS**

"Topology of the Real Milnor Fiber for Isolated Singularities", with R. dos Santos and N. Dutertre, To Appear, Contemporary Mathematics.

"Self-conjugate Vectors of Immersed 3-manifolds in R6", Topology and its Applications, 2011.

"Conjugate Vectors of Immersed Manifolds," Real and Complex Singularities, 1-12, Contemp. Math., 459, Amer. 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, Amer. 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.

GRANTS

Summer 2007:

Summer 2002:

PRESENTATIONS

"Duality of Immersed Manifolds", Workshop of Singularities in Geometry and Applications, Bedlewo, Poland, May 2011.

"How to Destroy the World Through Number Theorey", Pi Mu Epsilon, Jacksonville, FL, April 2011.

"Fractals from Root-solving Techniques", MAA Florida Regional Meeting, Orlando, FL, February 2011.

"Bitangencies on Higher Dimensional Immersed Manifolds", 11th International Workshop on Real and Complex Singularities, ICMC-USP, Sao Carlos, Brazil, 2010.

"Curves and Surfaces from 3-D Matrices", First Coast MAA Sectional Meeting, Jacksonville, FL, January 2010 and MAA Florida Regional Meeting, Gainesville, FL, February 2010.

"Self-Conjugate Vectors on Immersed 3-Manifolds in R

"What is Elliptic Curve Cryptography?", First Coast MAA Sectional Meeting, Jacksonville, FL, January 2009 and MAA Florida Regional Meeting, Fort Meyers, FL, February 2009, Key Note Talk, Embry-Riddle Undergraduate Mathematics Conference, Daytona, FL, April 2010.

"Singularities of the Tangential Gauss Map", 10th International Workshop on Real and Complex Singularities, ICMC-USP, Sao Carlos, Brazil, July 2008.

"Visualizing Milnor's Fibration Theorem", MAA Florida Regional Meeting, Lakeland, FL, March 2008.

"The Geometry of Conjugate Vectors", 9th International Workshop on Real and Complex Singularities, ICMC-USP, Sao Carlos, Brazil, July 2006.

"Visualizing Root Approximations", Student MAA Chapter Meeting, Jacksonville University, October 2005.

"Reconstructing Surfaces from their Outlines", Keynote talk, Florida Northeast Regional MAA Meeting, Jacksonville University, April 2005.

"The Geometry of Flecnodal Normals", 8th International Workshop on
Real and Complex Singularities, LUMNY, Marseille, France, July 2004.

"Building a Web Component for Explorations in
Mathematics", The 14th International Conference on College
Teaching and Learning, Jacksonville, April 2003.

"Invariance of the Diagonal Contribution in a Bitangency Formula", 7th International Workshop on Real and Complex Singularities, ICMC-USP, Sao Carlos, Brazil, July 2002.

"Squishin' Stuff: The Mathematics of Data Compression," Graduate Student Seminar, University of North Florida, October 2001.

"Fancy Ways to Connect the Dots," Graduate Student Seminar, University of North Florida, September 2000.

"Lights and Shadows: The Mathematics of Vision," Math/Stat Club Presentation, University of North Florida, February 2000.

"Singularities of the Binormal Surface," Contributed Paper, Joint Mathematics Meeting, Washington D.C., January 2000.

"Using the Web and WebCT in ‘Explorations in Mathematics’," Contributed Paper, Joint Mathematics Meeting, Washington D.C., January 2000.

"Lights, Shadows, and Stick Figures: The Mathematics of Vision," Seminar, Jacksonville University, April 1999.

"The Fourth Dimension," Seminar, Jacksonville University, April 1999.

"Bitangencies on Curves and Surfaces," MAA Florida Regional Conference, Panama City, March 1999.

"Semi-Simple Web Page Creation," Colloquium, University of North Florida, February 1999.

"A Bitangency Theorem for Surfaces in Euclidean Four-Space," Seminar, Fairfield University, July 1998.

"Apparent Contours of Surfaces," Job Talk, University of North Florida, April, 1998.

"Bitangencies on surfaces in Euclidean Three-Space," Shapes of Surfaces Seminar, Brown University, March, 1998.

"A Bitangency Theorem for Surfaces in Euclidean Four-Space," Geometry Seminar, Brown University, March, 1998.

"Contact Between Circles and Surfaces," Shapes of Surfaces Seminar, Brown University, November, 1997.

"A Counterexample to a Conjecture on the Coefficients of a Bounded Univalent Function," AMS National Meeting, Washington D.C., April, 1993.

**MISCELLANEOUS**

**2000:** Picture design for MAA recruitment advertisement.

**2000:** Picture design for MAA recruitment decal.

**1998:** Picture design for Brown University mathematics
graduate program
brochure.

PROFESSIONAL SERVICE

**University Committees**

- College of Arts and Sciences - Budget and Planning Committee - 2007, 2008
- Selection Committee for the Undergraduate Teaching Award
finalists
- 2002, 2008

- Research Grant Allocation Committee - 2000, 2001, 2008

**Department Committees**

- Promotion and Tenure By-Laws Committee (chair), 2006-2007
- Search Committee, 2004, 2005, 2006, 2007
- Academic Resource Committee - 2000 (chair), 2001
- Undergraduate Committee - 2003, 2005- (chair in 2010)

- Graduate Committee - 2004

- Liaison Committee - 1998, 1999 (chair), 2004

- Professional Development - 1999

2005-2010: Undergraduate Director, Department of Mathematics and Statistics.

2005-2010: Faculty Advisor, Math/Stat Club

**2001-2003:** Coordinator for the computer-based college
algebra.

**1999-2002:** Faculty Advisor, Sigma Kappa Brendo

TEACHING

**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.

- Business Calculus - F 01
- Calculus I - F 98, F 99, F 00, Su 04

- Calculus II - F 96, Sp 01, Su 03, F 04, F 05, Su 06, F 06, Su 07, Su 08, F 08
- Calculus III - F 97, Sp 02, Sp 03, F 03, Su 05, Sp 08, Su 09, Sp
10, Su 10, F 11

- Capstone - Sp 06, Sp 07, F 07, Sp 08, F 09, Sp 10
- College Algebra - Sp 99, Su 99, F 99, Sp 00, Su 00, F 00, F 03

- Complex Analysis - Sp 02
- Cryptography - Sp 09
- Explorations in Mathematics - F 99, Sp 02, F 02, Sp 04, F 04, F
05, F 06, F 11

- Foundations in Mathematics - Sp 05
- Geometry for Middle School Teachers - F 01, F 02, F 05, F 06, F
07, F 08, F 09, F 10, F 11

- Honors Calculus II - Sp 05
- Honors Explorations - Sp 06
- Linear Algebra - Sp 96, F 10

- Math Enhancement for Elementary School Teachers - Su 02
- Modern Geometry - Sp 00, Sp 07, Sp 09
- Partial Differential Equations - F 10

- Precalculus - Sp 99
- Topology - F 98
- Trigonometry - Su 02
- Vector Analysis - F 03, F 07

- Complex Analysis (independent study) - Sp 02
- Computer Vision - Sp 04
- Differential Geometry - Sp 99
- Numerical Analsys - F 04
- Scientific Computing - Sp 01, Sp 03, F 09

- Alex Aftuck - "Weil Pairing on Elliptic Curves with Applications to Cryptography", defended Summer 2011.

- John Metcalf - "Cusp Detection using Wavelets", defended Spring 2005.
- Derek Wray - "The Apparent Contour and Edge of Stationary and Rotating Surfaces", defended Summer 2000.

PROFESSIONAL ASSOCIATIONS

Mathematical Association of America

American Mathematical Society

Last updated, 9/15/11