Interactions of Classical and Numerical Algebraic Geometry

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

Algebraic geometry is a classical discipline which has for many years been situated at the intersection of algebra, number theory, several complex variables, and geometry in all its incarnations. The advent of personal computing, and more so the development of software for symbolic computation, introduced a new facet of the discipline; it was suddenly possible to carry out computations far too sophisticated to be handled manually. More recently, a numerical approach to algebraic geometry was pioneered, largely driven by the work of Sommese, Verschelde, and Wampler. This new field is aptly known as numerical algebraic geometry. The fundamental technique of this field, known as homotopy continuation, provides a numerical means of tracking the changing geometry resulting from algebraically morphing one system of polynomial equations into another. The ubiquity of polynomial systems throughout the sciences and engineering means that the techniques of numerical algebraic geome try may be used to solve problems arising in many different disciplines, such as kinematics, chemistry, economics, robot vision, and power electronics. It has recently been realized that the techniques of numerical algebraic geometry may be used to study problems in classical algebraic geometry as well. The purpose of this conference is to bring together classical and numerical algebraic geometers in a lively discussion forum to spark joint efforts between these two communities. The intersection of these two fields is ripe for rapid growth fueled by joint work, so it is the hope of the organizers that these interactions will help to yield important advances along this front. The conference will take place at the University of Notre Dame from May 22 to May 24, 2008. There will be 13 lectures over those three days, given by eminent scholars from both communities and from various locations throughout Europe and the U.S. As this field seems poised to spawn many new avenues of research, the participation of young mathematicians will be actively sought.