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,

Timetable:
Lecture 1: Tuesday, 23/03 18.00-19.30 MSK
Lecture 2: Thursday, 25/03, 18.00-19.30 MSK
Lecture 3: Tuesday, 30/03, 18.00-19.30 MSK
Lecture 4: Thursday, 01/04 18.00-19.30 MSK

The registration for the course (obligatory for organizational purposes) is available at
https://indico.eimi.ru/event/278/registrations/54/.
http://cvgmt.sns.it/event/630/