BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:"Sphere packings\, Fourier interpolation\, and modular forms"
DTSTART:20180328T123000
DTSTAMP:20260509T025354Z
UID:a06c2ed2ab10188c6b63b57659c872d709292e36891c8af63f02c5d6
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Maryna Viazovska\nThe sphere packing problem asks for t
 he densest configuration of non-intersecting open unit balls at the Euclid
 ean space. This classical geometric problem is solved only in dimensions 1
 \, 2\, 3\, 8\, and 24.  In this talk\, we will present a solution of the 
 sphere packing problem in dimensions 8 and 24. It seems that each dimensio
 n has its own features and requires a different approach. One method of es
 timating the density of a sphere packing from above was suggested by H. Co
 hn and N. Elkies in 2003. Their approach is based on Fourier optimization.
  Namely\, they showed that the existence of a function satisfying certain 
 inequalities for the function itself and for its Fourier transform leads t
 o an upper bound of the density of a sphere packing. Using this method Coh
 n and Elkies were able to prove almost sharp bounds in dimensions 8 and 24
 . We will show that functions providing exact bounds can be constructed ex
 plicitly. The key ingredient of our construction is the theory of modular 
 forms.
LOCATION:BSP 234 https://plan.epfl.ch/?room==BSP%20234
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR