Symplectic Structures in Geometry, Algebra and Dynamics
Collaborative Research Centre TRR 191
A1, A2, A3, A5, A6, A7, A8
B1, B2, B3, B4, B5, B6, B7, B8
C1, C2, C3, C4, C5, C6, C7
Algebra, Combinatorics & Optimization
C2: Algorithmic symplectic packing
(completed in the first funding period 2017-2020)
The aim of this project is to develop algorithmic tools for simplex packings that stem from the ball packing problem in symplectic topology. We want to formulate these packing questions as optimization problems so that recent, advanced algorithmic tools from combinatorial optimization (mixed integer non-linear programming, semidefinite optimization) can be used in this context. The insight gained from this experimental work should serve as the basis for further theoretical study. A major challenge, both computationally and theoretically, is the computation of packing widths in dimension greater than four.
Impressum Institution of DFG, MI University of Cologne, FM Ruhr-University Bochum and MI University of Heidelberg