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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.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20210111-C-Dostert.html
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