Special Seminar: Mansfield -- Moving Frames and Noether’s Theorem

Elizabeth Mansfield, University of Kent 

Moving Frames and Noether’s Theorem 

Thursday 27th Aug 15:05-15:55pm, Eastern Avenue Lecture Theatre.  

"Moving frames" or "repere mobile" are associated with the name of Elie Cartan, although
the ideas are older, and were used to solve a variety of equivalence problems in
differential geometry.  Recent reformulations, in particular the seminal work of Fels
and Olver, have freed the ideas to allow for a wider variety of applications, for
example in computer vision and Lie group invariant numerical schemes, and also to be
able to compute effectively with differential invariants and their differential
relations in symbolic computation.  

In this talk, I will give an overview of moving frames as they are now conceived.  The
application discussed will be to the Calculus of Variations, specifically, the
derivation and structure of Euler Lagrange equations arising from variational problems
having a Lie group symmetry.  I will also discuss the interplay between the moving frame
and the conservation laws that arise via Noether’s theorem.  

The talk is written for a non expert audience.