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Warren Weckesser
www.warrenweckesser.net

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Research Interests

• Software development for scientific applications
• Mathematical modeling
• Dynamical systems
• Multiple time scale systems and perturbation methods

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

• Senior Research Associate, School of Mathematics and Statistics, University of Sydney, Fall 2007
• Assistant Professor, Department of Mathematics, Colgate University, 2001-2007
  
• 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.
  

Industrial Positions

• Systems Engineer, FACT, Inc., 1986-1991. Developed several key components of a manufacturing information management system, including a discrete event simulation for scheduling work flow in a factory, and a database management system in a client-server operating system (QNX).

Grants

• NSF: RUI: Reduced System Computing for Singularly Perturbed Differential Equations, 2005-2007.

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).
11. VFGEN: A Code Generation Tool, J. Numerical Analysis, Industrial and Applied Math., 3(1-2) 151-165 (2008). [Link]
12. Bifurcations of mixed-mode oscillations in a stellate cell mode (with Martin Wechselberger), Physica D, to appear (2009).

Preprints

• Homoclinic clusters and chaos associated with a folded node in a stellate cell model (with Martin Wechselberger), submitted, 2008
• A new conserved quantity for the Kermack-McKendrick epidemic model (with Dan Schult), submitted, 2009

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
• Cardiff A cellular automaton-based reaction diffusion model.
• Other assorted scripts, programs and web applications used for teaching and research.

Presentations

• A New Conserved Quantity for the Kermack-McKendrick Epidemic Model
  • Computational and Applied Mathematics Colloquium, Penn State Department of Mathematics (September, 2008)
• The Kermack-McKendrick Integral Equations: An Introduction
• CCMA Luncheon Seminar, Penn State Department of Mathematics (September, 2008)
• VFGEN: A Code Generation Tool for Vector Fields
  • Canadian Applied and Industrial Mathematics Society minisymposium on New software for the numerical solution of differential equations, Second Canada-France Congress, Montreal (June 2008)
• The Kermack-McKendrick SIR Epidemic Model (parts 1 and 2)
  • Sydney Dynamics Group at the Unversity of Sydney and the University of New South Wales, Sydney (2007)
• Reduced System Computing and MMOs
  • SIAM Dynamical Systems Conference, Snowbird (2007)
• Reduced System Computing for Singularly Perturbed Differential Equations
  • The University of Sydney Applied Mathematics Seminar, Sydney (2007)
  • 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)

Copyright © 2007 Warren Weckesser