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
Stabilization of the inverted linearized pendulum
by high frequency vibrations
(with Mark Levi),
SIAM Review, 37(2), 219-223 (1995)
A ball rolling on a freely spinning turntable,
American Journal of Physics, 65(8), (1997)
[PDF]
Numerical computation of canards
(with J. Guckenheimer and K. Hoffman), Int. J. Bif. Chaos, 10, 2669-2687
(2000)
[PDF]
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)
Non-holonomic systems as singular limits for rapid oscillations
(with Mark Levi), Ergodic Theory and Dynamical Systems,22(5), 1497-1506 (2002)
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]
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]
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.)
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]
Bifurcations of relaxation oscillations near folded saddles
(with J. Guckenheimer and K. Hoffman), Int. J. Bif. Chaos15(11), (2005).
Submitted Papers
Stability of the relative equilibria of a class of
mechanical systems with rotational symmetry, submitted.