Discrete Geometry

Abstract

The 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:

• Extremal problems concerning convex lattice polygons. (Imre Bárány)
• Universally optimal configurations of points on spheres. (Henry Cohn)
• Polytopes, Lie algebras, computing. (Jesús A. De Loera)
• On incidences in Euclidean spaces. (György Elekes)
• Few-distance sets in $d$-dimensional normed spaces. (Zoltán Füredi)
• On norm maximization in geometric clustering. (Peter Gritzmann)
• Abstract regular polytopes: recent developments. (Peter McMullen)
• Counting crossing-free configurations in the plane. (Micha Sharir)
• Geometry in additive combinatorics. (József Solymosi)
• Rigid components: geometric problems, combinatorial solutions. (Ileana Streinu)
• Forbidden patterns. (János Pach)
• Projected polytopes, Gale diagrams, and polyhedral surfaces. (Günter M. Ziegler)
• What is known about unit cubes? (Chuanming Zong)

There were 16 shorter talks in the afternoon, an open problem session chaired by Jesús De Loera, and two special sessions: on geometric transversal theory (organized by Eli Goodman) and on a new release of the geometric software Cinderella (Jürgen 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.