# Program

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:
To advance research in the field, paying particular attention to its role within mathematics; and
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

**Keywords and Mathematics Subject Classification (MSC)**

**Primary Mathematics Subject Classification**No Primary AMS MSC

**Secondary Mathematics Subject Classification**No Secondary AMS MSC

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 |