Tilmann Wurzbacher
Multisymplectic geometry and dynamics - a case study
I will first discuss the notion of "(dynamical) Hamilton-DeDonder-Weyl equations" generalizing Hamilton's equations on symplectic manifolds and Volterra's equations in classical field theory at the same time. Then I will specialise to a surprising example : two-plectic geometry and dynamics on the six-sphere. It is well-known that the octonionic structure on an 8-dimensional real space yields a closed three-form and a non-integrable almost-complex structure on the six-sphere. We present joint work with Maxime Wagner, notably concerning its non-flatness, automorphisms and dynamics.
