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DESCRIPTION: In the first part of the talk\, I present how semidefinite pro
 gramming methods can provide upper bounds for various geometric packing pro
 blems\, such as kissing numbers\, spherical codes\, or packings of spheres 
 into a larger sphere. When these bounds are sharp\, they give additional in
 formation on optimal configurations\, that may lead to prove the uniqueness
  of such packings. For example\, we show that the lattice  E  8  is the uni
 que solution for the kissing number problem on the hemisphere in dimension 
 8. However\, semidefinite programming solvers provide approximate solutions
 \, and some additional work is required to turn them into an exact solution
 \, giving a certificate that the bound is sharp. In the second part of the 
 talk\, I explain how\, via our rounding procedure\, we can obtain an exact 
 rational solution of a semidefinite program from an approximate solution in
  floating point given by the solver. This is a joined work with David de La
 at and Philippe Moustrou. 
DTSTAMP:20210105T145600
DTSTART:20210111T160000
CLASS:PUBLIC
LOCATION:online
SEQUENCE:0
SUMMARY:Maria Dostert (Royal Institute of Technology): Exact semidefinite p
 rogramming bounds for packing problems
UID:107739187@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20210111-C-Dos
 tert.html
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