Luigi De Masi,

University of Padova,

Title: Min-max theory for minimal surfaces

Abstract: Existence and regularity of minimal surfaces (i.e. stationary points for area functional) with various boundary conditions has been an active topic of research for the last decades.

Although minimizing methods usually provide existence of solutions for some kinds of boundary constraints, they may produce just trivial solutions when dealing with different topological/boundary conditions; in that cases, one has to rely on different ways to obtain a critical point for a suitable functional. Min-max methods have been successfully used for some of these problems.

In this talk I will explain the basic ideas of min-max theory applied to the problem of finding a minimal surface in a container $\mathcal{M} \subset \mathbb{R}^3$ which meets the boundary with a fixed angle.

This is based on a joint work with Guido De Philippis.

Simone Steinbruechel

University of Leipzig

Title: Boundary regularity for 2-dimensional area minimizing currents at higher multiplicity boundary points

Abstract: We study the Plateau Problem, that is to find the surface with least area among those spanning a fixed boundary, in the language of integral currents. As those are very general objects, the question of existence changes into the one of regularity. This has been studied since the 60’s and various results are proven since then. In this talk I will summarize the state of the art as well as present our new point of view where we allow the 1d boundary (of a 2d area minimizing current) to be counted several times. This is a joint work with C. De Lellis and S. Nardulli.

Luca Benatti

Title: Various concepts of mass in General Relativity

Abstract: In recent years, the field of Mathematical General Relativity has witnessed the rise of numerous definitions of mass. These include the oldest and most famous ADM mass, the Hawking mass, the isoperimetric mass and the isocapacitary mass. In this talk, we aim to organise all these concepts, show how they are related, and prove, for some of them, classic theorems like the Positive Mass Theorem and the Riemannian Penrose Inequality. This is a work in preparation, joint with M. Fogagnolo and L. Mazzieri.

Alberto Roncoroni

Politecnico di Milano

Title: Rigidity results for the critical p−Laplace equation

Abstract: https://drive.google.com/file/d/1HXtRr0HMT1YPvyrGM6hn2QWlh9FD5THd/view?usp=sharing

Mattia Fogagnolo

Scuola Normale Superiore Pisa

Title: Some aspects of substatic manifolds

Abstract: I will present some recent advances about geometric inequalities in substatic manifolds.

Namely, I will discuss a sharp Heintze-Karcher inequality in this class and describe what happens when equality is achieved.

This is based on joint works with Andrea Pinamonti.

Silvia Ghinassi

University of Washington - Seattle

Title: Lower dimensional structure of purely unrectifiable sets

Abstract: Purely unrectifiable sets are, by definition, sets that are not “seen” by Lipschitz graphs. We investigate the finer structure of some self similar 1-dimensional purely unrectifiable sets, aiming to “quantify” how unrectifiable those sets can be.

The talk will cover work (very much) in progress, joint with Blair Davey and Bobby Wilson. Alternatively, it could be seen as a love note to the 4-corner Cantor set.