Optimal control problems lead to Hamilton-Jacobi Bellman (HJB) differential equations in many space variables for finding the cost function to be optimized. This beautiful connection has not generally led to effective numerical methods because grid based solutions of partial differential equations in n variables generally […]

Submitted by Larry Guth (MIT) The Kakeya problem is an open problem in Euclidean geometry, and it was a central theme in the 2014 IPAM long program, Algebraic Techniques for Combinatorial and Computational Geometry. It is elementary to state, but it’s also a model for […]

This article was written by Roja Bandari, who graduated from UCLA in 2013 with a PhD in Electrical Engineering As a participant in the 2010 IPAM program “Networks and Network Analysis for the Humanities,” I formed an appreciation for IPAM’s ability to connect scholars of […]

By combining quantum chemistry with artificial intelligence (AI) or Machine Learning, core participants of the long program, Navigating Chemical Compound Space for Bio and Materials Design, achieved a scientific breakthrough expected to aid in exploring chemical compound space, i.e. the virtual space populated by all […]