Posted in
Speaker:
Maryna Viazovska
Affiliation:
Berlin Math. School, HU Berlin
Date:
Wed, 01/06/2016 - 14:15 - 15:15
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar In this talk we will present a solution of the sphere packing problem in dimensions
8 and 24. In 2003 N. Elkies and H. Cohn proved that the existence of a real function
satisfying certain constrains leads to an upper bound for the sphere packing constant.
Using this method they obtained almost sharp estimates in dimensions 8 and 24. We
will show that functions providing exact bounds can be constructed explicitly as
certain integral transforms of modular forms. Therefore, the sphere packing problem
in dimensions 8 and 24 is solved by a linear programming method.
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