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24/05/2005, 16:30 — 17:30 — Amphitheatre Pa1, Mathematics Building

Eric A. Carlen, *School of Mathematics, Georgia Inst. of Technology*

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The symmetry of minimizers of variational problems

Physical systems often "relax" to a state of "minimal energy", and finding these minimal energy configurations of the system is a problem in the calculus of variations. Quite often, the solutions, that is, the minimizing configurations, have a special symmetry property that is not an obvious consequence of the energy functional being minimized. How does this symmetry arise? Can we explain it in mathematical and physical terms? A large number of questions in mathematics arise in this way, and it is a very active field of research. In this lecture we shall present several examples, some with recently obtained answers, and others that are still open.