Richard Montgomery, Mathematics Professor (Coordinates. Email: rmont ufigureitout edu. Office phone: 8314594841 (very rarely answered). Office: 4120 McHenry


Publications
Classes.
vita ( 2012)

R. Montgomery, Deer Creek, Spring, maybe 2010


finding the Math Dept on McHenry's 4th floor is non-trivial
the windows of McHenry


recommended math books :
Math sites for classical geometry :
Random beautiful math facts


N body : animations, etc
subRiemannian
videoed lecture(s).
wiki found my cat

Students ; and (some) of their theses
Collaborators

photos , physics, paddling photos, paddling
a great kayak videos (short)
more paddling
quotes
Memorium. Lars. 2009.


Ph.D. Students.

all graduated from UCSC with the exception of Bor.

for some student theses
go here

Corey Shanbrom (2013). thesis: Two Problems in Sub-Riemannian Geometry, now (*) at Cal. State Univ. Sacramento.
Wyatt Howard (2013). co-advised with V. Ginzburg. thesis: The Monster Tower and Action Selectors. now at Santa Clara.
Alex Castro (2010). thesis: Chains and Monsters. now on leave from PUC (Rio de Janeiro) as of Nov 2015
Vidya Swaminathan (2008). thesis: A Comparison of Two Methods of Resolution: Blow up and Prolongation.
William C. McCain (2007) (deceased)
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.
now at Universidade Federal de Pernambuco Recife,
Kurt Ehlers, (1995). thesis: The Geometry of Swimming and Pumping at Low Reynolds Number.
now at Tahoe Meadows Community College, and Desert Research Institute. Girija Mittagunta, (1994). (co-advised with Tudor Ratiu.)
thesis: Reduced Spaces for Coupled Rigid Bodies and Their Relation to Relative Equilibria
Patrick Tantalo, (1993), (co-advised with Tudor Ratiu.)
thesis: Geometric Phases for the Free Rigid Body with Variable Inertia Tensor.
at UCSC, Computer Science/ Engineering,

Gil Bor, (1991) [ unofficial ], official advisor: Marsden. UC Berkeley. thesis: Non-self dual solutions to the Yang-Mills equations over the four-sphere. Now at CIMAT, Guanajuato , Mexico. ****
(*) `now' means to the best of my knowledge as of November 1, 2015.

Master's Students

Chris Lebailly, (2013)

Research Blurb

(ammended Sept. 2012:)For nearly 15 years my primary mathematical obsession has been the planar zero-angular momentum three body problem. The basic question within that problem is still open after 344 years of work. Arbitrarily close to a bounded (eg. periodic) solution, does there exist an unbounded solution?

My methods are primarily those of differential geometry, so I might be called an applied differential geometer. Calculus of variations, dynamical systems, a bit of Lie group theory, and a smidge of topology often arise in my papers. Algebraic geometry has been sneaking in, due to the influences of blow-up on my work with Zhitomirskii and the birth of a K3 inside the planar 4 body problem.

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'.

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updated, Sept. 12, 2012