Wed, 08.11.2017, 17:15 |
The sphere packing problem in dimensions 8 and 24Mathematisches KolloquiumSpeaker:
Prof. Dr. Maryna Viazovska, École Polytechnique Fédérale de LausanneRoom:
S2|14 /24## Zuvor findet um 16:45 Uhr die Teerunde in Raum 244 des Mathematikgebäudes (S2/15), Schlossgartenstaße 7, statt.The sphere packing problem is to find an arrangement of non-overlapping unit spheres in the $d$-dimensional Euclidean space in which the spheres fill as large a proportion of the space as possible. 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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Fachbereich Mathematik

Technische Universität Darmstadt

Schlossgartenstraße 7

64289 Darmstadt