Dennis Sullivan, "The algebra of Poincare duality and statistics for Navier Stokes"
Channel: Danny Calegari
Date: 2013-05-13

Talk in the joint Dynamics/CAMP/Nonlinear PDE seminar at the University of Chicago, May 1, 2013.

Abstract: If the pieces of differential graded algebra hold together as they should, one obtains a tower of finite dimensional ODE's related by semiconjugacies [i.e., maps that commute with time evolution] that are derived from the Navier Stokes PDE in 3D -- which is itself used to model incompressible Newtonian fluid motion. Using these ODEs one can show the existence of measures at the top of the tower which project to consistent stationary measures for the ODE of each model in the tower. One can calculate algebraically the ODEs by algorithms that depend only on the combinatorics of cellular
decompositions. These ODEs can be treated numerically to compute stationary measures.