B.A., 1990, Northwestern University, Honors, Phi Beta Kappa
Ph.D., 1996, University of Minnesota, Dynamical Systems
Numerical and theoretical methods of dynamical systems. This includes global bifurcations for one-, two, and
three-dimensional diffeomorphisms, and finite dimensional noninvertible maps and relations. I also study differential equations modeling pattern
formation in materials science, chemistry, and biology. This includes the process of spinodal decomposition in metal alloys modeled by the
Cahn-Hilliard equation and animal coat pattern formation modeled by reaction-diffusion equations with Turing instabilities. It also includes
modeling and analysis in computational neuroscience.
- A classification of explosions in dimension one. Ergodic Theory and Dynamical Systems to appear, with J.A. Yorke.
- Explosions in dimensions one through three. Rendiconti del Seminario Matematico, Torino, 65(1), 2007, with K.T. Alligood and J.A. Yorke.
- Complex transient patterns on the disk. Discrete and Continuous Dynamical Systems, Series A, 15(4):1049-1078, 2006, with J. P. Desi and T. Wanner.
- Three-dimensional crisis: Crossing bifurcations and unstable dimension variability. Phys. Rev. Lett. 96, 244103 (2006), with K.T. Alligood and J.A. Yorke.
- Dynamics of noninvertibility in delay equations. Discrete and Continuous Dynamical Systems Special Issue, 768-777, 2005, with E. Barreto, S. Schiff, and P. So.
The Structure of Synchronization Sets for Noninvertible Systems. Chaos, 14 (2): 249-262, 2004, with K. Josic.
The geometry of chaos synchronization. Chaos, 13(1):151-164, 2003, with E. Barreto, K. Josic, C. Morales, and P. So.
Pattern Formation in a Nonlinear Model for Animal Coats. Journal of Differential Equations, 191(1):143-174, 2003, with T. Wanner.
Limits to the Experimental Detection of Nonlinear Synchrony. Physical Review E, 65, 2002, 046225, with P. So, E. Barreto, K. Josic, and S.J. Schiff.
Explosions: Global bifurcations at heteroclinic tangencies. Ergodic Theory and Dynamical Systems, 22(4):953-972, 2002, with K. Alligood and J. Yorke.
Professional Awards and Invitations
September 1, 2006-August 31, 2010 "Mechanisms of wave propagation in neuronal tissue" (co-PI) CRCNS grant, NIH-NIMH Grant Number R01-MH79502, $1,269,896.
September 1, 2006-August 31, 2010, Undergraduate research in computational mathematics (co-PI), CSUMS, DMS, NSF, $1,057,257.
- 2008-10, Secretary/Treasurer of the SIAM Activity Group on Dynamical Systems (SIAG/DS) (Elected 2007)
- 2008-10 Editor-in-Chief, DSWeb Magazine.
- 2008-present, SIAM Dynamical Systems Activity Group Liason to SIAM News.
- 2004-present, Section Chief Editor, Tutorials, DSWeb. Organized the DSWeb biennial student contest in 2005 and 2007, including presenting awards at the SIAM Conference on Applications of Dynamical Systems, Snowbird, UT.
- Midwest Dynamical Systems Conference, Bloomington, IN, October, 2008.
- Computational Topology and Dynamics Workshop, Bozeman, MT, August, 2008.
- July, 2008, Association for Women in Mathematics (AWM) professional mentor for two early career women mathematicians.
- Seminar, UMBC, Baltimore, MD, May, 2008.
- Spring Topology and Dynamics Conference, Milwaukee, WI, March, 2008.
- Seminar, George Washington University, Washington, DC, February, 2008.
- Colloquium, William and Mary College, Williamsburg, VA, November, 2007.
- Seminar, Mathematics, Marymount University, Arlington, VA, October, 2007.
- Colloquium, Mathematisches Institut, Universität Erlangen-Nürnberg, Germany, July, 2007.
- Seminar, Technische Universität München, Germany, July, 2007.
- Workshop on Dynamical Systems and Applications, Banff International Research Station, June 22-24, 2007.
- May, 2007, Association for Women in Mathematics (AWM) professional mentor for an early career woman mathematician.
- Women in Scientific Domains, George Mason University, May, 2007.
- From Microscopic to Macroscopic: Mechanisms Underlying Epileptic Seizures, Center for Theoretical Physics, Ann Arbor, MI, May, 2007.
- The Diverse Universe of Model Analysis Special Session, SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, May, 2007.
- Colloquium, Bioinformatics Department, George Mason University, April, 2007.
- Colloquium, George Mason University, April, 2007.
- Special Session on Dynamical Systems, AMS Spring Southeastern Section Meeting, Davidson, NC, March, 2007.
- Seminar, Center for Neural Dynamics, George Mason University, March, 2007.
- Colloquium talk and modeling course visiting lecture, GeorgeWashingtonUniversity, February, 2007.
- Colloquium, Virginia Tech, November, 2006.
- Graduate student seminar, October, 2006.
- Public lecture, Osher Lifelong Learning Institute at GeorgeMasonUniversity, October, 2006.
- August, 2006, Academic Career Panelist, Summer Program for Women in Mathematics, George Washington University.
- Measurable Dynamics, Theory and Applications, Banff International Research Station, August 5-10, 2006.
- Topology in Dynamical Systems Session, Summer Conference on Topology and its Applications, Statesboro, GA, July 6-9, 2006.
- Formation and Dynamics of Patterns in Evolution Equations, AIMS' Sixth International Conference on Dynamical Systems, Differential Equations and Applications, Poitiers, France, June 25-28, 2006.
- Seminar, University of Augsburg, Germany, June 12, 2006.
- Neural Dynamics Group and Graduate student seminars GeorgeMasonUniversity, April, 2006.
- Applied Dynamics Seminar, University of Maryland, April, 2006.
- CM/AMO Seminar, The University of Michigan, March, 2006.
- Department Seminar, MontclairState, February, 2006.
- Mathematical Biology Seminar, NJIT, February, 2006.
- Applied and Computational Math Seminar, Georgia Tech, January, 2006.
- Society for Neuroscience, November, 2005.
- Computational Neuroscience, Madison, WI, July, 2005.
- Pattern Formation and Wave Dynamics in the Brain, SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, May, 2005.
- MBI Young Researchers Workshop, OhioStateUniversity, March, 2005.
- Differential Equations Seminar, University of Maryland, BaltimoreCounty, December, 2004.
- Colloquium, SwarthmoreCollege, October, 2004.
- GeorgeWashingtonUniversity Summer Program for Women in Mathematics, WashingtonDC, June 29, 2004.
- Fixed Points, Periodic Orbits and EquilibriumStates in Hyperbolic Dynamics Session, 5th International Conference on Dynamical Systems and Differential Equations, Pomona, California, June 16-19, 2004.
- Spring Topology and Dynamics Conference, Birmingham, Alabama, March 25-27, 2004.
- Maryland-Penn State Workshop on Dynamical Systems, College Park, MD, March, 2004.
January 1, 2004- December 31, 2005 "A dynamical framework for transient neuronal patterns" (Principal Investigator) NIH-NIMH Grant Number R03MH67659, $140,569.
Spring, 2002 College of Arts and Sciences Junior Faculty Awards in the Social Sciences and Sciences for "Noninvertibility in Biological Models."
Summer, 2002 Summer Research Support for Tenure Track Faculty for "Starcy Gels, Sea Shells, and Animal Coats."
Research project with doctoral student Robert Allen (advisor Flavia Colonna).
- 2007-08 undergraduate students: Hanein Edrees and John Price, as part of the URCM program, joint with Thomas Wanner. They are presenting a poster of their results at the SIAM Annual Meeting in July, 2008.
Advisor, Anne Costolanski, Masters Thesis, "Explosion points in skew maps," July, 2007. She was awarded the department's outstanding graduate student award. Current doctoral students: Robert Reznick (PhD student, SCS), Richard Tatum (PhD student, SCS).
Advisor, Tyler White, GMU-funded undergraduate research apprenticeship, $1100 Summer, 2005, renewed $1100 Fall, 2005. He was also a research assistant. Advisor for his honors senior thesis, "A neurological model for shell pattern formation," Spring, 2006.
Master's Project advisor, Karen Crossin, December, 2003.
Robert Allen, Undergraduate Senior Thesis, 2003.