Browsing by Author "Schürmann, Achill"
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- ItemThe contact polytope of the Leech lattice(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Dutour Sikiri´c, Mathieu; Schürmann, Achill; Vallentin, FrankThe contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we classify the facets of the contact polytope of the Leech lattice up to symmetry. There are 1, 197, 362, 269, 604, 214, 277, 200 many facets in 232 orbits.
- ItemMini-Workshop: Exploiting Symmetry in Optimization(Zürich : EMS Publ. House, 2010) Liberti, Leo; Schürmann, Achill; Sotirov, RenataThe feasible regions of mathematical optimization models quite often exhibit a high degree of symmetry. In recent years, several groups of researchers have independently worked on algorithmic approaches to exploit such symmetries in a variety of contexts. Many of the techniques that have been developed are related or rely on similar computational tools. The workshop brought together researchers working on symmetry aspects in different areas of optimization. The exchange of state-of-the-art knowledge between these areas lead to identification of important directions for future research activities.
- ItemOptimal and Near Optimal Configurations on Lattices and Manifolds(Zürich : EMS Publ. House, 2012) Grabner, Peter; Saff, Edward B.; Schürmann, AchillOptimal configurations of points arise in many contexts, for example classical ground states for interacting particle systems, Euclidean packings of convex bodies, as well as minimal discrete and continuous energy problems for general kernels. Relevant questions in this area include the understanding of asymptotic optimal configurations, of lattice and periodic configurations, the development of algorithmic constructions of near optimal configurations, and the application of methods in convex optimization such as linear and semidefinite programming.