Professor & Chair
Burton Hall 309
cgole at smith.edu
My research interests are in the theory of dynamical systems as it applies to Hamiltonian systems and Mathematical Biology. Dynamical systems is the mathematical theory that studies time evolution of systems. They have been used to model many systems from physics, economics, biology etc. The theory's claim to fame is to be the proper setting to the mathematical notion of chaos.
Hamiltonian systems, is a subfield of dynamical systems that includes Celestial Mechanics and all physical, mechanical systems that conserve energy. A pendulum without friction is a simple example of Hamiltonian system. My research in that field was centered on finding periodic orbits for these systems. I helped develop variational methods that arise from decomposing the time evolution of the system into finite time steps (leading to symplectic maps). In this context, I came across some strange objects that I baptised ghost tori.
My Mathematical Biology interest is in plant pattern formation (phyllotaxis). One well publicized phenomenon is the very frequent occurrence of Fibonacci numbers of spirals in sunflowers, pine cones and many other plants. My colleagues (P. Atela, S. Douady, J. Dumais, S. Hotton) and I have studied different mathematical models where one can prove theorems explaining this phenomenon (as well as others lesser known phenomena). In collaboration with the Smith Botanic Garden, we also created an exhibit "Plant Spiral: Beauty You Can Count On". It has toured Europe and is now accessible in virtual form on our Phyllotaxis website, which also contains a variety of informations about phyllotaxis.
I was born in France and raised partly in Northen Africa. I also lived two years in Mexico. Before coming to Smith College, I held positions at U. of Minesota, ETH (Zurich), SUNY Stony Brook and UC Santa Cruz. I directed the Smith Geneva JYA program in 2003-04. I like playing jazz piano and reading. I live in Northampton with my wife Liz and daughter Marguerite.
Courses taught Recently
Introduction to Analysis (MTH243), Calculus (MTH111 & 114) Modern Algebra (MTH 233)
- Symplectic Twist Maps (World Scientific, 2001)
- A Dynamical System for Plant Pattern Formation: Rigorous Analysis (with P.Atela and S. Hotton), J. Nonlinear Sci. Vol. 12 , Number 6 (2002)
- Lagrangian systems on hyperbolic manifolds (with Boyland, P.) Ergodic Theory & Dynamical Systems , 19, (1999)
- A Note on Carnot Geodesics in Nilpotent Lie Groups (with R. Karidi) J. of Dyn. & Control Sys. (1995)
- Periodic orbits for Hamiltonian systems in cotangent bundles, Trans. AMS. Vol. 343, number 1, (1994)
- More publications