Lecture course Geometric flows of networks

Matteo Novaga, Universita' di Pisa, Alessandra Pluda, Universita' di Pisa,

Abstract: The study of geometric flows is a very flourishing mathematical field and geometric evolution equations have been applied to a variety of topological, analytical and physical problems. In particular, in the last decades a great attention has been devoted to the analysis of the mean curvature flow. In this series of lectures we will introduce the notion of curvature flow of curves and networks, describing the possible approaches to this geometric evolution. We will present the state of the art of the problem, from the short time existence and uniqueness to a description of the long time behavior and singularity formation. We will conclude the course with some recent extensions to higher order flows and a list of open problems.

Program: - Lecture 1: Formulation of the curvature flow of curves and networks and preliminary results. - Lecture 2: Short time existence and uniqueness of the motion by curvature of networks. - Lecture 3: Monotonicity formula and analysis of singularities. - Lecture 4: Elastic flow of curves and networks: State of the art and open problems.

The lectures will be held in ZOOM,