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Mathematical Sciences Research Institute

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Program

Discrete and Computational Geometry August 11, 2003 to December 19, 2003
Organizers Jesús A. De Loera, Herbert Edelsbrunner, Jacob E. Goodman, János Pach, Micha Sharir, Emo Welzl, and Günter M. Ziegler
Description Humans have been fascinated with discrete spatial structures for centuries. Yet most people today are not aware of the rich mathematical theory and the wealth of applications that polyhedra, arrangements of lines, sphere packings, tilings, and simplicial complexes offer.

Discrete and Computational Geometry deals with the structure and complexity of discrete geometric objects as well with the design of efficient computer algorithms for their manipulation. This area is by its nature interdisciplinary and has relations to many other vital mathematical fields, such as algebraic geometry, topology, combinatorics, and probability theory; at the same time it is on the cutting edge of modern applications such as geographic information systems, mathematical programming, coding theory, solid modeling, and computational structural biology.

This program will bring together mathematicians and computer scientists interested in problems in this area, with two chief goals:

  1. To advance research in the field, paying particular attention to its role within mathematics; and
  2. To enhance the interaction between the study of purely combinatorial properties of geometric structures and the design and analysis of efficient algorithms that construct and manipulate those structures.

Here is a sample of topics we plan to cover in which substantial activity has recently taken place:

  • Extremal and reconstruction problems for polytopes
  • Lattice polytopes and connections to algebraic geometry and optimization
  • Geometric computing in structural molecular biology
  • Volume estimation of polyhedra
  • Computational questions in topology
  • Oriented matroids and combinatorial convexity
  • Curve and surface reconstruction
  • Geometric graph theory and problems of Erdös type
  • Geometric deformation, rigidity of structures, realization spaces
  • Optimal triangulations and meshes
  • Arrangements of surfaces

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Programmatic Workshops
August 20, 2003 - August 29, 2003 Introductory Workshop in Discrete and Computational Geometry
October 13, 2003 - October 17, 2003 Mathematical Foundations of Geometric Algorithms
November 17, 2003 - November 21, 2003 Combinatorial and Discrete Geometry