Topology, Geometry and Data Seminar -: Dan Burghelea

Title: Dynamics and persistence. Lecture II: Persistence invariants for a topological closed one form(why computer friendly)

 

Speaker: Dan Burghelea - The Ohio State University

 

Abstract: Dynamics consider flows on some metrizable spaces; many of such flows of interest in science are “ locally conservative”. For such flows the “dynamical elements” of interest are : rest points, visible trajectories between rest points and closed trajectories. 

 

Morse-Novikov theory considers as mathematical model for such flow, “locally conservative” vector fields on a smooth manifolds (i.e. smooth vector field whose trajectories minimize an “action”, equivalently closed 1- form, Lyapunov for the vector field) and, in generic situation, relates the elements of its dynamics to the topology of the underlying manifold. This relation is derived via invariants not “computer friendly” and the mathematical hypotheses on such models are often too restrictive for possible applications. 

 

The Alternative to Morse-Novikov theory I propose partially addresses these drawbacks; it extends the class of flows considered by classical MN theory and derives a similar relationship via “computer friendly” invariants of interest both in mathematics and outside mathematics. This talk is a brief summary of AMN-theory.