Configuration Spaces: Geometry, Topology and Combinatorics
January 16 – 27, 2017
Configuration spaces have a long history in mathematics and occur in many branches and applications. We mention points in affine space and the relation with braids, linkages, points on Riemann surfaces, etc.
The aim of the project is the studyof a variety of configuration spaces via smooth (and also discrete) Morse theory and to determine their topological, geometrical and combinatorial properties. We include configuration spaces with metric constraints (with certain distances fixed) and geometric constraints.
Our approach has already led to a substantial progress in the case of potential functions, such as Coulomb Energy and Signed Area. We intend use in this project Discrete Morse theory, Small cover-type cell decompositions and Voronoi diagrams for a deeper understanding of the configuration spaces. The main framework of the proposed research program is an interplay between smooth and discrete settings. 


Giorgi Khimshiashvili (Ilia State University)
Gayane Panina (St Petersburg University)
Dirk Siersma (University of Utrecht)