2006–2007 thematic program:
Applications of Algebraic Geometry

Many results and algorithms that were originally developed for abstract algebraic geometry are now applied, or have the potential to be applied, to a diverse assortment of research efforts. Techniques originally thought to be of interest only to the algebraic geometry community have led to exciting new results in biology, control theory, economics, and optimization. Scientists in fields ranging from finance to bioinformatics are learning about ideals, varieties, and the algorithms used to compute with these objects. The 2006–2007 annual program Applications of Algebraic Geometry will bring mathematicians who develop theorems and algorithms in algebraic geometry together with researchers from other disciplines—including computer science, economics, statistics, and engineering—that can benefit from those developments, enhancing interaction, generating new applications, and spurring further progress.

One of the original goals in the development of algebraic geometry was to understand the behavior of curves and surfaces in three dimensions; recent theoretical and technological advances in areas such as robotics, computer vision and computer-aided design and manufacturing have revitalized the practical roots of what had come to be regarded as a particularly esoteric branch of mathematics. Connections between algebraic geometry, computational complexity and coding theory have been a rich source of new results through the decades. In recent years, methods from algebraic geometry have found roles in many novel settings. For example, there have been many exciting new developments in continuous, discrete, and dynamic optimization using ideas and concepts with origins in algebraic geometry; mixed symbolic and numeric methods have become a reality. The thematic program will explore these and many other innovative applications of algebraic geometry.

The program is divided into three quarters, each consisting of two six-week periods of concentration:
Fall Quarter
    Algorithms in Algebraic Geometry (September 5–October 13)
    Software for Algebraic Geometry (October 16–November 24)
Winter Quarter
    Optimization and Control (January 8–February 16)
    Emerging Applications—Statistics, Economics, Bioinformatics, etc (Feb 19–March 30)
Spring Quarter
    Complexity, Coding, and Communications (April 2–May 11, 2007)
    Nonlinear Computational Geometry (May 14–June 22, 2007)

Each quarter of the program will include a tutorial and two workshops. In the first quarter, the two workshops cover algorithms and software, with a particular eye towards applications. In the second and third quarter, the workshops cover applications in optimization, control, statistics, economics and bioinformatics, coding, complexity, communications and computational geometry.

Organizing Committee: Dimitris Bertsimas (MIT), Pablo Parrilo (MIT), Michael Stillman (Cornell), Bernd Sturmfels (Berkeley), Madhu Sudan (MIT), and Rekha Thomas (Washington).