Conference on "Symmetries of Differential Equations: Frames, Invariants and Applications"

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

This grant provides travel support for graduate students, postdocs, and invited lecturers to participate in the Conference on "Symmetries of Differential Equations: Frames, Invariants and Applications" to be held at the School of Mathematics, University of Minnesota, May 17-19, 2012. The general conference theme is inspired by the lifetime research achievements of Professor Peter Olver, but focus will be on current advances, promising directions, and novel applications. The main topics addressed are symmetries of differential equations and variational problems, with special emphasis on moving frames, Cartan theory of differential forms and invariant theory. Also Hamiltonian systems and integrable systems including solitons will be treated, as well as applications of symmetry based methods to image processing, fluid mechanics and elasticity. The organizing committee is: Niky Kamran (Mathematics, McGill University), Gloria Mari Beffa (Mathematics, University of Wisconsin), Guillermo R. Sapiro (Electrical and Computer Engineering, University of Minnesota), and Willard Miller, Jr, (Mathematics, University of Minnesota). Detailed information is available on the website http://math.umn.edu/conferences/olver/ and results of the meeting, including abstracts, slides and a panel discussion, will also be posted there. In conjunction with the conference the on line journal SIGMA will publish a special issue entitled ``Symmetries of Differential Equations: Frames, Invariants and Applications'' with the conference organizers as guest editors, http://www.emis.de/journals/SIGMA/SDE2012.html. The general theme of the conference is the exploitation of symmetries of mathematical and physical systems to deduce properties of these systems. More specifically, most physical theories are expressed in terms of differential equations and the mathematical symmetries of these equations can be exploited to reach important conclusions about the systems that obey the equations. The meeting comes at a propitious time - an explosion of new results and new methods in symmetry analysis, with applications ranging over geometry, differential equations, computer vision, numerical analysis, mechanics, and physics, make this an ideal time to assemble the leading experts, and promising younger researchers to assess the rapid advances in the area, reach a consensus on what are the most important problems, and evaluate the most promising directions for further advance. We expect the conference to be a major event in the history of this research area.