Hamilton-Jacobi (HJ) Partial Differential Equations (PDEs) were originally introduced during the 19th century as an alternative way of formulating mechanics. Since then, these PDEs have received a considerable amount of attention because they arise in many scientific areas and real-life applications beyond physics. For instance, HJ PDEs appear in optimal control, stochastic optimal control, random media, probability, random dynamical systems, large deviations theory, mean field games, optimal transport, optimization in imaging sciences and machine learning.
Applications that involve HJ PDEs in a high-dimensional (and possibly infinite-dimensional) setting lead to challenging computational problems. Although a large literature is available on HJ PDEs, many challenges remain both from a mathematical and computational point of view. A lot of interactions have occurred over recent decades between these areas thanks to their connection to HJ PDEs. The subject is currently on the verge of becoming central to many new areas of applications, and progress in tackling Hamilton-Jacobi equations could lead to important advances in several fields. The main goal of this long program is to leverage synergy between different fields to advance mathematical theory and algorithms to solve real-life problems.
The program will open with one week of tutorials, presented by some of the main organizers. These tutorials will provide an introduction to the major themes of the entire program and connect the themes of the four workshops. The goal is to introduce a common language and build a foundation for the participants of this program who have diverse scientific backgrounds.
During the weeks between workshops, participants in residence will develop collaborations; we expect fruitful discussions especially between domain scientists, algorithm developers and pure and applied mathematicians.
Craig Evans (University of California, Berkeley (UC Berkeley), Mathematics)
Fariba Fahroo (Air Force Office of Scientific Research (AFOSR), Computational Math)
Wilfrid Gangbo (University of California, Los Angeles (UCLA))
Adam Oberman (McGill University, Mathematics and Statistics)
Stanley Osher (University of California, Los Angeles (UCLA), Mathematics)
Panagiotis Souganidis (University of Chicago, Mathematics)
Claire Tomlin (University of California, Berkeley (UC Berkeley))