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Moving frames and the calculus of variations: analytical and numerical solutions up to dimension 2

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In this talk I will give a gentle introduction to the theory of moving frames and its applications to the calculus of variations. Through the use of some simple running examples, I will show how the moving frames machinery can make life very easy when we have to deal with 1D Lagrangian that possesses a Lie group symmetry. In the second part of the talk I will present a conjecture we have been trying to solve, regarding the use of Lie group integrators in order to numerically solve 2D variational problems. If time permits, I’ll finish giving some information about how the smooth and discrete cases can be treated in a single more general setting.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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