Moving Currents - On the Lie Transport Equation and a Rademacher Type Theorem

Explore the extension of classical transport theory to k-currents in R^d in this 31-minute seminar by Paolo Bonicatto at the Hausdorff Center for Mathematics. Delve into the Lie transport equation and its applications in modeling defects in plastic materials. Examine the challenges and recent results of extending transport/continuity equations to generalized k-dimensional surfaces. Learn about the Lie derivative of currents, the relationship between continuity and transport equations, and the ongoing research project with Giacomo Del Nin and Filip Rindler. Cover topics including the theory of currents, subclasses of currents, the lead derivative, and rectifiability. Gain insights into this cutting-edge mathematical research and its potential implications for understanding complex material behaviors.

Introduction
Outline
Motivations
Theory of currents
Subclasses of currents
The lead derivative
The transport equation
Does the converse hold
The proof
Rectifiability