Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Prof. Elizabeth Mansfield,School of Mathematics, Statistics & Actuarial Science, University of Kent, UK
Introduction to Moving Frames
Time & Venue:
2015.8.9 16:30-17:30 N702
I will give a brief overview, suitable for graduate students, of the definition and construction of the Lie group based moving frame, and then I will talk about applications to the equivalence problem, to the invariant evolution of curves, to solving invariant ODE, to the algebra of differential invariants, and to the variational calculus. I will finish by briefly introducing recent work with Gloria Mari Beffa: a construction of multispace, a manifold which contains both finite difference and Taylor polynomial approximations (ie the jet bundle) to functions defined on surfaces. This will be used to construct a finite difference Lagrangian for shallow water systems which not only has all the correct continuum limits, but is invariant under a discretisation of the particle relabelling symmetry, needed for the conservation of potential vorticity.
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