SPECIAL SEMESTER
ON DISCRETE AND COMPUTATIONAL GEOMETRY
1 July - 31 December 2010

+ REUNION CONFERENCE
27 February - 2 March 2012

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Program overview

 

Discrete and Computational Geometry arose as a new field within the past twenty-five years, through an amalgamation of the old field of discrete geometry and the nascent field of computational geometry. It is now a very active area of research, on the interface between pure mathematics and theoretical computer science, which is devoted to understanding the structure and complexity of discrete geometric structures as well as the design and analysis of geometric algorithms for their manipulation. Key examples of the objects studied are arrangements (of lines, curves, and their higher-dimensional analogues), polytopes and polyhedra, tilings, packings and coverings, oriented matroids, simplicial complexes, geometric graphs, transversals to families of convex sets, Voronoi diagrams, etc.

 
Discrete and Computational Geometry bears strong relations to well-established mathematical areas
such as algebra (e.g., toric varieties, symmetry groups, real algebraic geometry), topology (e.g., combinatorial manifolds, realization spaces), probability theory (e.g., randomization techniques, geometric probability), and combinatorics (e.g., extremal graph and hypergraph theory). These relations give Discrete and Computational Geometry the solid footing to serve as the language and mathematical foundation for attacking problems in many applied fields. Examples include mathematical programming (relations between the efficiency of linear and integer programming algorithms and the structure of high-dimensional polyhedra), geographic information systems (geometric data structures to identify nearest neighbors, contour line extraction, range searching, and map overlays of massive data sets), solid modeling (optimal triangulations and good quality meshes), crystallography (lattices, tilings and discrete periodic structures), and computational biology (alpha-shape methods in the prediction of protein structure and function). On the other hand, classical problems such as Keplers conjecture and Hilberts third problem, as well as classical works by mathematicians such as Minkowski, Steinitz, Hadwiger, and Erdős can be considered part of the heritage of the area.

The goal is to bring together a mix of senior and junior colleagues to advance research in the field. Several fields in mathematics make intensive use of discrete geometric objects and methods either as tools or as important special cases of their theory. We aim to foster interaction between researchers in these rather diverse fields, to discuss recent progress and to communicate new results. We would like to put an emphasis on the exchange of ideas, approaches, and techniques between various areas of Discrete Mathematics and Computer Science and on the identification of new tools from other disciplines which can be used to solve geometric problems. The program is funded by the Swiss National Science Foundation, by EPFL, and by the Chair of Combinatorial Geometry. Applications are welcome (see below).

Program activities

Most of the activities will take place at the Bernoulli Interdisciplinary Center, at the Swiss Federal Institute of Technology in Lausanne (EPFL) between the end of August and the end of December 2010. To register to any of the first two events, visit the individual webpages.

Throughout the program, there will be regular weekly seminars, special workshops, and lecture series at the Bernoulli Institute. Full and partial support for long-term participants is available, and those interested are encouraged to fill out an online application at the bottom of this page. Support for individual workshops will also be available, and may be applied for through the online application for each workshop. We are especially interested in applicants who are interested in becoming core participants and participating in most of the activities between September 1 and December 31, but also give consideration to applications for shorter periods. Funding for participants is available at all academic levels, though recent PhD's, graduate students, and researchers in the early stages of their career are especially encouraged to apply.

 

Bernoulli lectures

The lectures will be held in room CM 4 (click here to see the map)

If you have any questions, please do not hesitate to contact janos.pach@epfl.ch, Christiane De Paola .

Scientific organizing committee

János Pach, EPFL, Lausanne, Switzerland.

Emo Welzl, ETH, Zurich, Switzerland.