Richard Montgomery, Mathematics Professor, emeritus, UCSC, (Coordinates. Email: rmont ufigureitout edu. Office: 4140 McHenry

Math Publications
Oct 12, 2023: they did the coin flip experiment!
Classes taught.
vita ( 2022)

2023 07 20 MercedHole Hands

Merced River, July 20 or 21, 2023. Photo courtesy of Toby Roessingh

Ph.D. Student
unpublished math
recommended math books .
Beautiful math videos (via Gil Bor)


    Life and work in academia
A Vulture at the University House & ...
    (commentary on that Vulture)
The Windows of McHenry
Gutting the Science Library and the resulting
    Senate Resolution , and SJ Merc News Op-Ed

    On and Off the River
Fig Trees & Bare Feet
Plan B
David Gill swims the Stan
Three Trips (with Lars)
Memorium. Lars. 2009.

the all-administrative Univeristy direction the UCSC seems to be driving hard for.
world statistics visualization warning! optimism abounds here!
a favorite blog

N body : animations, etc
Falling Cats
Open Problem Lists

video. slides. audio.
a podcast interview on whitewater in CA go to episode 20

Editorial Boards (only one!)


some student theses

Photos and a video. Mostly of paddling
    physics, paddling
    more paddling
the Big One, on the San Lorenzo
        (and quite short!)

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