Marsden Memorial Lecture Series
The 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.
2016, June 19 (Banff International Research Station): The Constraint Manifold of General Relativity
Richard Schoen (University of California, Irvine)The global study of the space of solutions of the Einstein constraint equations goes back to work of Jerry Marsden and co-workers in the early 1970’s. Since that time the subject has evolved in interesting ways. First it has been possible to localize the deformation theory in certain cases to deform solutions inside a chosen region without changing them outside. A second issue which arises in the deformation theory is a derivative loss problem which occurs when one attempts to place a manifold structure on the constraint space of solutions with a finite degree of differentiability. In this general lecture we will give an overview of these issues and developments.
2015, June 10 (École Polytechnique Fédérale de Lausanne, Switzerland): From Euler to Born-Infeld, Fluids and Electromagnetism
Yann Brenier (École Polytechnique, Paris)As the Euler theory of hydrodynamics (1757), the Born-Infeld theory of electromagnetism (1934) enjoys a simple and beautiful geometric structure. Quite surprisingly, the BI model which is of relativistic nature, shares many features with classical hydro- and magnetohydro-dynamics. In particular, I will discuss its very close connection with Moffatt’s topological approach to Euler equations, through the concept of magnetic relaxation.
2014, April 7 (Instituto Nacional de Matematica Pura e Aplicada [IMPA], Rio de Janeiro): Geometric discretization for computational modeling
Mathieu Desbrun (Caltech)
Geometry is at the foundation of many physical theories, even if it is often obfuscated by their formulations in vectorial or tensorial notations. When computational simulation is needed, leveraging geometric formulations of physical models can potentially lead to numerical methods with exact preservation of momenta arising from symmetries, good long-term energy behavior, and robustness with respect to the spatial and temporal resolution---only if one can preserve some of the most defining continuous structures in the numerical realm. In this talk, we will review a number of structure-preserving discretizations of space and time, from discrete counterparts of differential forms and symmetric tensors on surfaces, to finite-dimensional approximation to the diffeomorphism group and its Lie algebra. A variety of applications (from masonry to magnetohydrodynamics) will be used throughout the talk to demonstrate the value of a geometric approach to computations.
2013, June 10 (Isaac Newton Institute): Nonlocal Evolution Equations
Peter Constantin (Princeton University)
Peter Constantin conducts research on turbulent convection, the physics of exploding stars and other topics related to fluid dynamics. The author of 140 papers and two books, he has given invited talks to three international mathematical congresses. Constantin also has made extended visits to research institutions around the world, including the Institute for Advanced Study in Princeton, N.J., the Isaac Newton Institute for Mathematical Sciences in Cambridge and the Weizmann Institute of Science in Israel. He is a fellow of the Alfred P. Sloan Foundation, the American Institute of Physics, and the Society for Industrial and Applied Mathematics.
2012, July 25 (Fields Institute): An Octahedral Gem Hidden in Newton’s Three Body Problem
Richard Montgomery (University of California, Santa Cruz)
Richard Montgomery’s primary mathematical obsession is the planar zero-angular momentum three body problem. The basic question inside that problem is still open after 344 years of work. Arbitrarily close to a bounded (eg. periodic) solution, does there exist an unbounded solution?
He completed his PhD under Jerry Marsden at Berkeley in 1986.
2011, July 20 (ICIAM, Vancouver): Introduction to Marsden & Symmetry
Alan Weinstein (University of California, Berkeley)
Alan Weinstein is a Professor of the Graduate School in the Department of Mathematics at the University of California, Berkeley. He was a colleague of Jerry Marsden throughout Jerry’s career at Berkeley, and their joint papers on “Reduction of symplectic manifolds with symmetry” and “The Hamiltonian structure of the Maxwell-Vlasov equations” were fundamental contributions to geometric mechanics.