Flows of Vector Fields: Classical and Modern - Camillo DeLellis

Explore the classical and modern theories of flows of vector fields in this comprehensive analysis seminar lecture. Delve into the textbook examples, classical theory, and modern approaches presented by Camillo DeLellis, Faculty and IBM von Neumann Professor at the Institute for Advanced Study's School of Mathematics. Examine key concepts such as the DiPerna-Lions approach, commutator estimates, and Ambrosio's superposition principle. Investigate well-posedness "almost everywhere" and linearity in the context of vector field flows. Gain insights into the work of Jabin, Caravenna-Crippa, and their contributions to a.e. uniqueness in this advanced mathematical exploration.

Intro
Main point
The classical theory III
The textbook example
Textbook example II
Classical theory IV
Modern theory
Modern III
Modern IV
Commutator estimate
The DiPerna-Lions approach III
Postmodern?
Well-posedness "almost everywhere", answers
Back to the DiPerna-Lions theory
Linearity and superposition
Ambrosio's superposition principle
Jabin, Caravenna-Crippa a.e. uniqueness