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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. 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.