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Modular forms and sphere packing

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Maryna Viazovska
Humboldt Universiät Berlin
Fri, 2017-05-26 14:00 - 14:50
MPIM Lecture Hall

In this talk we will give an application of modular forms to the sphere
packing problem. First, we will explain the Cohn-Elkies linear
programming bound for the best packing constant in Euclidean space.
Next, we will show that the linear programming problems corresponding to
dimensions 8 and 24 can be solved explicitly. As a byproduct of our
method, we will prove a new type of interpolation formula for the
Schwartz functions. Finally, using this  approach we  will present  the
solution of the sphere packing problem in dimensions 8 and 24.


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