**The next seminar:** ** New advances on the existence and regularity of Brakke’s mean curvature flows**

**Lecturer: ****Salvatore Stuvard**

**Date & Time: 28.11.2023 , 12:00 AM**

**Place:** Department of Mathematics,University of Milan

**Abstract: **In this talk, I aim at giving an overview of what we know, and also of what we don’t know, about the existence and the regularity properties of Brakke flows. These are measure-theoretic, weak solutions to the mean curvature flow capable of describing the evolution of surfaces through singularities and topology changes, with applications ranging from Materials Science to Biology. If time permits, I will also try to explain how the analysis of the parabolic flow opens a new avenue of research into the regularity of its stationary, elliptic counterpart: minimal surfaces. Joint work with Yoshihiro Tonegawa (Tokyo Tech).