Tomorrow, there will be only a Monday *Colloquium* at 16:00. The Lecture at 14:15 by Raman Sanyal (From counting lattice points to counting free segments and back) had to be canceled and will be given at a later time. Invitation link: https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09 Time: Monday, Jan 11, 2021 - 16:00 h s.t. Colloquium: Maria Dostert (Royal Institute of Technology, Stockholm): Exact semidefinite programming bounds for packing problemsIn the first part of the talk, I present how semidefinite programming methods can provide upper bounds for various geometric packing problems, such as kissing numbers, spherical codes, or packings of spheres into a larger sphere. When these bounds are sharp, they give additional information on optimal configurations that may lead to prove the uniqueness of such packings. For example, we show that the lattice E8 is the unique 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 joint work with David de Laat and Philippe Moustrou. http://www.facetsofcomplexity.de/monday/WS-2020-21/index.html