Events

Abstract: TBA

Organizers: Prof. Antonio De Rosa, Prof. Alessandro Pigati

Funding: 

• ERC StG ANGEVA, project number: 101076411

• ERC StG MAGNETIC, project number: 101165368

Confirmed speakers: 

• Marco Badran - ETH Zurich

• Alessandro Carlotto - University of Trento

• Guido De Philippis - New York University

• Nicholas Edelen - University of Notre Dame

• Irene Fonseca - Carnegie Mellon

• Filippo Gaia - ETH Zurich

• Matilde Gianocca - ETH Zurich

• Yangyang Li - Univeristy of Chicago

• Fanghua Lin - New York University

• Paul Minter - University of Cambridge

• Connor Mooney - UC Irvine

• Robin Neumayer - Carnegie Mellon

• Reinaldo Resende - Carnegie Mellon

• Tristan Rivière - ETH Zurich

• Felix Schulze - University of Warwick

• Yannick Sire - Johns Hopkins University

• Luca Spolaor - UC San Diego

• Daniel Stern - Cornell University

• Federico Trinca - U British Columbia

• Bozhidar Velichkov - University of Pisa

• Xin Zhou - Cornell University

Program: 

All the talks take place in room 3-E4-SR03

9:30 Coffee

10:00 - 11:00

Elena Giorgi - Columbia University

Title: The nonlinear stability of black holes: an overview
Abstract: Black holes are the most striking predictions of General Relativity and are by now understood to be fundamental objects in our universe. In this talk, I will provide an overview of their mathematical properties, in particular concerning their stability as solutions to the Einstein equation, and give a bird’s-eye view of the recent proof of the nonlinear stability of the slowly rotating Kerr black holes (joint with Klainerman-Szeftel). 

11:15 - 12:15

Costante Bellettini - University College London

Title: PDE analysis on stable minimal hypersurfaces: curvature estimates and sheeting
Abstract: We consider properly immersed two-sided stable minimal hypersurfaces of dimension n. We illustrate the validity of curvature estimates for n \leq 6 (and associated Bernstein-type properties with an extrinsic area growth assumption). For n \geq 7 we illustrate sheeting results around "flat points". The proof relies on PDE analysis. The results extend respectively the analogous Schoen-Simon-Yau estimates (obtained for n \leq 5) and the Schoen-Simon sheeting theorem (valid for embeddings).

Lunch Break

14:00 - 15:00

Alberto Roncoroni - Politecnico di Milano

Title: On the stable Bernstein problem
Abstract: Click HERE

15:15 - 16:15

Luca Spolaor - UCSD

Title: On the boundary branching set of the one-phase problem
Abstract: I will discuss the boundary regularity for minimizers of the so-called Alt-Caffarelli problem and how it is related to a boundary unique continuation problem. This is joint work with L. Ferreri (SNS) and Bozhidar Velichkov (Pisa).

16:30 Greetings

Abstract: The workshop is the 11th edition of the traditional Pisa meeting, which started in 2001. It aims to collect the latest contributions from leading researchers in the field of Optimal Transport and its applications, and to provide a comprehensive overview of the remarkable and impressive developments in this evolving field in several theoretical and new applied directions. 

Abstract: The aim of the meeting is to build new bridges and to foster interactions between experts employing techniques proper of Geometric Measure Theory in different areas, including Calculus of Variations, Differential Geometry, Ergodic Theory, Fractal Geometry, Metric Analysis, Optimal Transport and PDE's.

Abstract: This is the second workshop of the UMI Group "Mathematics for Artificial Intelligence and Machine Learning" following the one held in Turin in November 2022. The workshop focuses on the interplay between mathematics, artificial intelligence and machine learning. The aim of the programme is to encourage mathematical research in these areas, to promote the dissemination of results and to facilitate interaction with other disciplines. Proposals for contributed talks are reserved for junior researchers; the presence of senior researchers is welcome. Participating and contributing is not restricted to UMI members, but is open to all interested researchers. Keynote speakers:

Fosca Giannotti, Scuola Normale Superiore, Pisa

Marc Mezard, Bocconi University, Milan

Tomaso Poggio, MIT, Cambridge

Alfio Quarteroni, Politecnico di Milano  

Abstract:  This goal of this workshop is to bring together international experts working at the interface between optimal transport, control theory for large-scale systems and their macroscopic approximations, and variational methods for problems formulated in measure spaces. Indeed, a wealth of recent theoretical-and application-oriented findings – notably in the fields of statistical learning, measure relaxations of variational problems and mean-field control – have brought to light new connexions between theses research fields. In this context, we want to contribute to the development of a meetings cycle in order to facilitate the propagation of new ideas and results in these lively domains, as well as to stimulate new collaborations around these topics which are currently investigated by neighbouring communities. This workshop will aim at covering three main thematic axes, which enjoy strong interconnections with one another and already produced fruitful interactions in recent times. The first of these segments is that of optimal transport theory, which has become instrumental in a growing number of applications and more theoretical mathematical fields, and plays a pivotal role in the foundations of many of the ensuing topics. The second is that of the macroscopic descriptions and control of multi-agent and many-body systems, which includes mean-field control problems, large-scale limits of cooperative dynamics and graphons, as well as continuous models for deep neural networks. The third and last one is that of resolution methods for variational problems in measure spaces, which can either arise from measure relaxations of classical variational problems or directly stem from the aforedescribed fields. Regarding its impact, this workshop will bring together researchers from at least 7 European countries, and is planned to be the sequel of a meeting taking at the Technische Universität München in April 2023, organised by Martin Burger, Massimo Fornasier, Gabriel Peyré and Giuseppe Savaré. As such, we believe that it has the potential to attract many postdoctoral and PhD students – both from France and abroad –, as well as fellow researcher and colleagues of the fields interested in participating to the gathering. We also think that main themes of the conference may be of interest for colleagues working in control theory, particle dynamics and PDE analysis at Aix-Marseille Université.