Warren Weckesser Assistant Professor

314 McGregory Hall Department of Mathematics Colgate University Hamilton, NY 13346

Tel: (315) 228-7228 Fax: (315) 228-7004 Email: wweckesser (at) mail.colgate.edu Web: math.colgate.edu/~wweckesser

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Research Interests

• Dynamical systems
• Multiple time scale systems and perturbation methods
• Mathematical modeling

Education

• Ph.D., Mathematics, Rensselaer Polytechnic Institute, 1997
  
• M.Eng., Computer and Systems Engineering, Rensselaer Polytechnic Institute, 1989
  
• B.S., Computer and Systems Engineering, Rensselaer Polytechnic Institute, 1986 (magna cum laude)
  

Honors

Graduate	Joaquin B. Diaz Prize, Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 1997 Department of Mathematical Sciences Fellowship, Rensselaer Polytechnic Institute, 1991-1993
Undergraduate	Tau Beta Pi, Engineering Honor Society Eta Kappa Nu, Electrical Engineering Honor Society Essie and Harriet Rader Scholarship, Rensselaer Polytechnic Institute

Academic Positions

• Assistant Professor, Department of Mathematics, Colgate University, 2001-present
  
• Assistant Professor, Department of Mathematics, University of Michigan, 1999-2001
  
• Postdoctoral Member, Institute for Mathematics and its Applications, 1997-1999.
      1997-1998 Theme: Emerging Applications of Dynamical Systems
      1998-1999 Theme: Mathematics in Biology
  
• Research Assistant, Rensselaer Polytechnic Institute, 1996-1997.
  
• Teaching Assistant, Rensselaer Polytechnic Institute, 1991-1996.
  
• Graduate Research Assistant, Center for Nonlinear Studies, Los Alamos National Labs, summer, 1994.
  

Grants

• RUI: Reduced System Computing for Singularly Perturbed Differential Equations, NSF Grant (DMS-0514468), 2005-2008.

Undergraduate Research

• 2002: Co-directed five undergraduates in the Cornell Summer REU Program; resulted in publication 8.
• 2003: Summer research with one student, funded by the Colgate NASC Division/Wolk Grant.
• 2004: Co-directed four undergraduates in the Cornell Summer REU Program.
• 2005: Summer research with two students, funded by the Colgate NASC Division.

Publications

1. Stabilization of the inverted linearized pendulum by high frequency vibrations (with Mark Levi), SIAM Review, 37(2), 219-223 (1995)
2. A ball rolling on a freely spinning turntable, American Journal of Physics, 65(8), (1997) [PDF]
3. Numerical computation of canards (with J. Guckenheimer and K. Hoffman), Int. J. Bif. Chaos, 10, 2669-2687 (2000) [PDF]
4. Global bifurcations of periodic orbits in the forced van der Pol equation (with J. Guckenheimer and K. Hoffman), in Global Analysis of Dynamical Systems, H. W. Broer, B. Krauskopf, G. Vegter, eds., Inst. of Physics Publ., Bristol, (2001)
5. Non-holonomic systems as singular limits for rapid oscillations (with Mark Levi), Ergodic Theory and Dynamical Systems, 22(5), 1497-1506 (2002)
6. The forced van der Pol equation I: the slow flow and its bifurcations (with J. Guckenheimer and K. A. Hoffman), SIAM Journal on Applied Dynamical Systems, 2(1), 1-35 (2003) [PDF]
7. Resonance in the menstrual cycle: a new model of the LH surge (with M. L. Zeeman and D. Gokhman), Reproductive BioMedicine Online, 7(3), (2003) [PDF]
8. The forced van der Pol equation II: canards in the reduced system (with K. Bold^*, C. Edwards^*, J. Guckenheimer, S. Guharay^*, K. Hoffman, J. Hubbard^*, and R. Oliva), SIAM Journal on Applied Dynamical Systems, 2(4) 570-608 (2003) [PDF]
   (^*Undergraduate student.)
9. Canards and horseshoes in the forced van der Pol equation, Equadiff 2003, Proc. of the Int. Conf. on Diff. Eq., Hasselt, Belgium, F. Dumortier, H. Broer, J. Mawhin, A. Vanderbauwhede, and S Verduyn Lunel, eds. World Scientific, 2005. [PDF]
10. Bifurcations of relaxation oscillations near folded saddles (with J. Guckenheimer and K. Hoffman), Int. J. Bif. Chaos 15(11), (2005).

Submitted Papers

• Stability of the relative equilibria of a class of mechanical systems with rotational symmetry, submitted.

Other Reports

• Symbolic dynamics in mathematics, physics and engineering (available at the IMA web site, http://www.ima.umn.edu/industrial/97_98/tufillaro.html; click on "Full article").

Software

• VFGEN: A Vector Field File Generator
• Other assorted scripts, programs and web applications used for teaching and research.

Presentations

• Reduced System Computing for Singularly Perturbed Differential Equations
  • The 5^th International Conference on Differential Equations and Dynamical Systems, University of Texas - Pan American (2006)
• Reduced System Computations and Bifurcations for Singularly Perturbed Differential Equations
  • Rensselaer Polytechnic Institute, Department of Mathematical Sciences (2006)
• The Surprising Vibrating Pendulum
  • Colgate Physics and Astronomy Seminar (2005)
  • Cornell Summer REU Smorgasbord Seminar (2004)
• Reduced Systems and Canards for Neuron Models
  • SIAM Dynamical Systems Conference, Snowbird (2005)
• Canards and Horseshoes in the Forced van der Pol Equation
  • Clarkson University, Dept. of Math. and Comp. Sci (2005)
  • University of Maryland, Baltimore County, Dept. of Math. and Stats. (2004)
  • Workshop on Structured Dynamical Systems, Mathematisches Forschungsinstitut Oberwolfach, Germany (2003)
  • Equadiff 2003, Hasselt, Belgium (2003)
  • SIAM Dynamical Systems Conference, Snowbird (2003)
• Canards and Horseshoes: A New Look at Classical Chaos
  • Colgate University Science Colloquium (2003)
• Periodic Orbits and Canards in Coupled Relaxation Oscillators
  • SIAM Dynamical Systems Conference, Snowbird (2001)
  • University of Michigan, Math Dept. (2000)
  • IMA, University of Minnesota (1999)
• Stability of the Whirling Modes of a Hanging Chain
  • University of Minnesota, Math Dept. (1998)
  • SIAM Dynamical Systems Conference, Snowbird (1997)
  • University of Vermont, Dept. of Mathematics (1997)
  • Boston University, Dept. of Mathemetical Sciences (1997)
  • Rensselaer Polytechnic Institute, Dept. of Math. Sci. (1997)

Professional Activity

• Journal Referee: SIAM J. Appl. Dyn Sys., Physica D, American Journal of Physics, Comm. Pure and Applied Math.
• AMS and SIAM member.