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N body : animations, open problems, links
vita ( 2009)
email: rmont at ucsc period edu ; phone:831- 459-4841
office: 4120 McHenry. ! moved summer 2011!
passages I like ...
A big influence on my career has been `classical' gauge theory: the geometry of a principal bundle with connection. Following the physicists Shapere, Wilczek and Guichardet, I explored the connections between gauge theory and questions in everyday (not high energy) physics and control such as how does how a cat, dropped from upside down, with zero angular momentum? Idealizing the cat to consist of only three mass points led me deep into the jungle of the three-body problem, where I have stumbling about in wonderment ever since.
Overview of research periods
1982-1988. Symplectic and Poisson reduction. What is the reduced space of the cotangent bundle of a principal bundle?
1986-1998. Falling cats. The isoholonomic problem. Realization that the isohol. problem is one of optimal control. Subriemannian geometry, culminating in the `abnormal geodesic' and a book titled `A tour of SubRiemannian Geometry'.
1999-2012 and on. Beginning with the rediscovery of Cris Moore's figure eight solution to the three body problem, Chenciner and I helped open up a mini-industry of `choreography' solutions to the N-body problem. My most general result here is the theorem that with the exception of Lagrange's orbit every zero angular momentum negative energy solution to the three body problem has instants of collinearity, or `syzygies'.
2002- 2011. Various problems and the interstices of singularity theory, geometry of plane-fields (distributions), and algebraic geometry, culminating in a book with Misha Zhitomirskii: `Points and Curves in the Monster Tower'.
Alex Castro (2010), UCSC.
Vidya Swaminathan (2008), UCSC
William C. McCain (2007), UCSC
Andrew Klingler, 1999. thesis: Stochastic Calculus and Eigenvalue bounds for Geometric Laplacians.
Alex Golubev, 1999. (co-advised with Viktor Ginzburg.) thesis: A Gray's theorem for Engel Structures.
Cesar Castilho, 1998.
(co-advised with Viktor Ginzburg.)
thesis: The Motion of a Charged Particle on a
Riemannian Surface under a Non-zero Magnetic Field
professor at: Departamento de Matematica Universidade Federal de Pernambuco Recife, PE 50540-740 Brazil
Kurt Ehlers, 1995.
thesis: The Geometry of Swimming and Pumping at Low Reynolds Number
email: email@example.com Reno Community College.
Girija Mittagunta, 1994.
(co-advised with Tudor Ratiu.)
thesis: Reduced Spaces for Coupled Rigid Bodies and Their Relation to Relative Equilibria
Patrick Tantalo, 1993, (UCSC)
(co-advised with Tudor Ratiu.)
thesis: Geometric Phases for the Free Rigid Body with Variable Inertia Tensor. Now a lecturer in Computer Science/ Engineering, UCSC.
Gil Bor, 1991 (Berkeley), ( unofficial student,
co-advised with Jerry Marsden.) thesis: Non-self dual solutions to the Yang-Mills equations
over the four-sphere.
Now at CIMAT, Guanajuato , Mexico.
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