Discrete Geometry

Abstract

The \emph{Discrete Geometry} workshop was attended by 53 participants from a wide range of geographic regions, many of them young researchers (some supported by a grant from the European Union). The morning sessions consisted of survey talks providing an overview of recent developments in Discrete Geometry: \begin{itemize} \item Extremal problems concerning convex lattice polygons. (Imre B\'ar\'any) \item Universally optimal configurations of points on spheres. (Henry Cohn) \item Polytopes, Lie algebras, computing. (Jes\'us A. De Loera) \item On incidences in Euclidean spaces. (Gy\"orgy Elekes) \item Few-distance sets in $d$-dimensional normed spaces. (Zolt\'an F\"uredi) \item On norm maximization in geometric clustering. (Peter Gritzmann) \item Abstract regular polytopes: recent developments. (Peter McMullen) \item Counting crossing-free configurations in the plane. (Micha Sharir) \item Geometry in additive combinatorics. (J\'ozsef Solymosi) \item Rigid components: geometric problems, combinatorial solutions. (Ileana Streinu) \item Forbidden patterns. (J\'anos Pach) \item Projected polytopes, Gale diagrams, and polyhedral surfaces. (G\"unter M. Ziegler) \item What is known about unit cubes? (Chuanming Zong) \end{itemize} There were 16 shorter talks in the afternoon, an open problem session chaired by Jes\'us De Loera, and two special sessions: on geometric transversal theory (organized by Eli Goodman) and on a new release of the geometric software Cinderella (J\"urgen Richter-Gebert). On the one hand, the contributions witnessed the progress the field provided in recent years, on the other hand, they also showed how many basic (and seemingly simple) questions are still far from being resolved. The program left enough time to use the stimulating atmosphere of the Oberwolfach facilities for fruitful interaction between the participants.