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SUMMARY:Gaussian energy minimization in high dimensions
DTSTART:20180612T151500
DTEND:20180612T161500
DTSTAMP:20260414T212004Z
UID:6c9c97b43b2d8b8794e896d96b3e081623046a114f9383c3ef75a664
CATEGORIES:Conferences - Seminars
DESCRIPTION:Matthew de Courcy-Ireland (Princeton University)\nWe discuss a
 n energy defined for configurations in Euclidean space and given by a Gaus
 sian interaction between each pair of points. Many other potential functio
 ns can be synthesized\, by the Laplace transform\, as a superposition of G
 aussians. The goal is to minimize energy over all configurations with a gi
 ven number of points per unit volume. Lower bounds for energy can be obtai
 ned by the linear programming method whenever one can produce an auxiliary
  function with certain properties. In the special dimensions 8 and 24\, Co
 hn-Kumar-Miller-Radchenko-Viazovska find the optimal such function and use
  it to solve the minimization problem exactly. In arbitrary dimension\, Co
 hn and I show how to make a suboptimal choice that leads to a surprisingly
  good bound. In the easy case where the Gaussian is not too steep\, and in
  the limit of high dimension\, this bound asymptotically matches the energ
 y that can be achieved by choosing a random lattice. For a more rapidly de
 caying Gaussian\, the problem is closely related to sphere packing\, and t
 here is a wider gap between our upper and lower bounds.
LOCATION:GR A3 31 https://plan.epfl.ch/?room==GR%20A3%2031
STATUS:CONFIRMED
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