Mathematical Conversations

The Mumford-Shah functional has been introduced by Mumford and Shah in 1989 as a variational model for image reconstruction. Since then, it has been widely studied both from a theoretical and an applied point of view. In this talk we will focus on regularity of minimizers, especially the famous Mumford-Shah conjecture. I will try to present the existence and regularity results up to today, and if time allows discuss some recent progress (joint work with Camillo De Lellis and Matteo Focardi).