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The Kakeya problem

Posted on 6/29/14 in Research Articles

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 […]

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Kakeya Figure

IPAM: Where Math Creates Connections

Posted on 12/8/13 in Research Articles

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 […]

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Exploration of Chemical Compound Space Unites Quantum Chemistry With Artificial Intelligence

Posted on 7/8/12 in Research Articles

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 […]

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ccs graph-2

Multiscale representation of macromolecular motion

Posted on 5/18/11 in Research Articles

How many variables do we need to describe macromolecular motion? The answer depends on the time and length scale of interest. By analyzing the geometry of the space defined by long molecular dynamics trajectories of macromolecular systems, we find that different regions of the configurational […]

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