My research interests are in the theory of dynamical systems. My earlier research concentrated on Hamiltonian systems and my more recent research is on 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 has been 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).
My main 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 Pau Atela, Jacques Dumais, Stéphane Douady, Scott Hotton, and I have studied different mathematical models where one can prove theorems explaining this phenomenon, among others. The concepts we introduced can be used to analyze plant data. In collaboration with the Smith Botanic Garden, we also created an exhibit "Plant Spiral: Beauty You Can Count On". It is now accessible in virtual form on our Phyllotaxis website, which also contains a variety of informations about phyllotaxis. My other biomathematical research project have included plasticity in the arm race between crabs and snails (with David Smith and students), and zebra fish neurogenesis (with Michael Baressi, Nessy Tania and students).
In recent years, I have been involved in the creation of the Concentration in Biomathematical Sciences at Smith, soon to become a 5 College certificate program, as well as the NSF funded 4 College Biomathematical Sciences Consortium, which I direct this year.
Personal Information 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, and the Paris JYA program in 2014-2015. You can often see me at the French and Spanish tables (mondays and Wednesdays at Duckett House). I like playing jazz piano and reading. I live in Northampton with my wife Liz.
- The possible and the actual in phyllotaxis: Bridging the gap between empirical observations and iterative models. Journal of Plant Growth Regulation 25: 313-323 (Hotton, S, V Johnson, J Wilbarger, K Zwieniecki, P Atela, C Golé, J Dumais (2006))
- 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)
Spiral patterns in a daisy. There are 21 spirals winding in one direction, 34 in the other. Find more about this in the Phyllotaxis website.