# Physics

## An Octahedral Gem Hidden in Newton's Three Body Problem (2012 Marsden Memorial Lecture)

Richard Montgomery, University of California, Santa Cruz will deliver a talk entitled, "An Octahedral Gem Hidden in Newton's Three Body Problem." The lecture will take place on July 25, 2012 at the Fields Institute, as part of the conference on "Geometry, Symmetry, Dynamics, and Control: The Legacy of Jerry Marsden."

Richard Montgomery received undergraduate degrees in both mathematics and physics from Sonoma State in Northern California. He completed his PhD under Jerry Marsden at Berkeley in 1986, after which he held a Moore Instructorship at MIT for two years, followed by two years of postdoctoral studies at University of California, Berkeley.

Montgomery's research fields are geometric mechanics, celestial mechanics, control theory and differential geometry and is perhaps best known for his rediscovery - with Alain Chenciner - of Cris Moore's figure eight solution to the three-body problem, which led to numerous new 'choreography' solutions. He also established the existence of the first-known abnormal minimizer in sub-Riemannian geometry, and is known for investigations using gauge-theoretic ideas of how a falling cat lands on its feet. He has written one book on sub-Riemannian geometry.

The PIMS Marsden Memorial Lecture Series is dedicated to the memory of Jerrold E Marsden (1942-2010), a world-renowned Canadian applied mathematician. Marsden was the Carl F Braun Professor of Control and Dynamical Systems at Caltech, and prior to that he was at the University of California, Berkeley, for many years. He did extensive research in the areas of geometric mechanics, dynamical systems and control theory. He was one of the original founders in the early 1970s of reduction theory for mechanical systems with symmetry, which remains an active and much studied area of research today.

The inaugural Marsden Memorial Lecture was given by Alan Weinstein (University of California, Berkeley) in July of 2011 at ICIAM in Vancouver.

## Gauge Theory and Khovanov Homology

After reviewing ordinary finite-dimensional Morse theory, I will explain how Morse generalized Morse theory to loop spaces, and how Floer generalized it to gauge theory on a three-manifold. Then I will describe an analog of Floer cohomology with the gauge group taken to be a complex Lie group (rather than a compact group as assumed by Floer), and how this is expected to be related to the Jones polynomial of knots and Khovanov homology.

## PIMS Board Meeting - Fall 2011

The PIMS 2011 Fall board meeting was held at the University of Saskatchewan. In addition to the board meeting, board members toured the Canadian Light Source facility.