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Gaussian Energy in High Dimensions
William Thurston Lectures| Speaker: | Henry Cohn, Microsoft Research and MIT |
| Related Webpage: | https://cohn.mit.edu |
| Location: | 1147 MSB |
| Start time: | Wed, May 14 2025, 3:10PM |
Sphere packing involves hard constraints: spheres are absolutely forbidden to overlap, and we don't care at all what they do otherwise. In many cases, soft constraints are more natural. For example, we could impose a repulsive force between some particles, with the repulsion decaying towards zero at infinity. If we scatter these particles throughout space and set them loose, how will they arrange themselves? More precisely, what is their ground state? In this talk, we'll examine a curious phase transition in our ability to analyze ground states in high dimensions.