Although geometry has been studied for thousands of years, the term of discrete geometry is of quite recent origin. Combinatorial geometry deals with the structure and complexity of discrete geometric objects and is closely related to computational geometry, which deals with the design of efficient computer algorithms for manipulation of these objects. This area is by its nature interdisciplinary and has relations to many other vital mathematical fields and also applications to computer science. The focus of this workshop will be on the study of discrete geometric objects, their combinatorial structure, stressing the connections between discrete geometry and combinatorics, number theory, analysis and computer science.
Specific topics will include extremal problems in combinatorial geometry, results on the number of incidence between points and lines (hyperplanes and etc.), applications of incidence bounds to combinatorial number theory and analysis, Erdos’ repeated and distinct distance questions, geometric graph theory and graph drawings, computational geometry, covering and packing problems, Helly type theorems and applications to clustering, convex polytopes, hyperplane arrangements, algebraic and topological methods in discrete geometry, combinatorics of convex sets, application of convex geometry to linear programming and optimizations.
(University of Michigan)
Gil Kalai (Hebrew University)
Janos Pach (Renyi Institute of Mathematics)
Jozsef Solymosi (University of British Columbia)
Emo Welzl (ETH Zürich)