Solving packing problems by linear programming

Solving packing problems by linear programming

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Maryna Viazovska , Humboldt University
Fine Hall 314

Part 1:  Optimal configurations of points on manifolds. Classical problems and unexpected solutions.   The sphere packing problem asks which biggest portion of the euclidean d-dimensional space can be covered by non-overlapping unit balls. In most dimensions d this question is believed be an extremely difficult combinatorial geometric problem. However, in dimensions 8 and 24 the sphere the sphere packing problem has a surprisingly simple solution based on linear programming bounds.The goal of this series of talks is to explain the ideas behind this solution.