Department of

August 2013 September 2013 October 2013 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 1 2 3 4 5 6 7 1 2 3 4 5 4 5 6 7 8 9 10 8 9 10 11 12 13 14 6 7 8 9 10 11 12 11 12 13 14 15 16 17 15 16 17 18 19 20 21 13 14 15 16 17 18 19 18 19 20 21 22 23 24 22 23 24 25 26 27 28 20 21 22 23 24 25 26 25 26 27 28 29 30 31 29 30 27 28 29 30 31

Monday, September 23, 2013

**Abstract:** After recalling the precise definition of a topological Hamiltonian dynamical system, I will sketch the proof of the 1-1 correspondence between topological Hamiltonian isotopies and topological Hamiltonian functions. I also show that this result has non-empty content by constructing a non-smooth topological Hamiltonian dynamical system (with support in a Darboux chart). We then shift gears and focus on two sample applications to 1) hydrodynamics (topological character of the helicity invariant, which measures the average asymptotic linking number of the flow lines of a divergence-free vector field) and to 2) Riemannian geometry (C^0-rigidity of the geodesic flows associated to a sequence of weakly uniformly converging Riemannian metrics).