Spring Topology and Dynamics Conference 2002, at the University of Texas at Austin on March 21-23, 2002

University Of Texas At Austin, Austin TX

Investigators

Abstract

DMS-0129227 Cameron M. Gordon The Department of Mathematics at the University of Texas at Austin will host the 2002 Spring Topology and Dynamics Conference. Now in its 36th year, this is the largest annual topology conference in the US. It has a broad scope that encompasses set-theoretic and general topology, continuum theory and dynamical systems, geometric group theory and geometric topology. It thus provides a unique forum for researchers in a wide range of disciplines within topology. There will be eight invited plenary one-hour lectures of a semi-expository nature, given by leading researchers in the areas covered. There will also be twenty invited half-hour lectures, together with 15-minute contributed talks, held in four parallel sessions. The invited speakers have been selected with the help of an advisory committee of experts in the various subfields. Topology is one of the major subdisciplines of mathematics, and, at just over a hundred years old, the youngest. It originated with Henri Poincare around 1900, who introduced it as a means of describing the qualitative behavior of certain physical systems (for example, our solar system), whose complexity renders a precise quantitative analysis too difficult. The wide range covered by the subject today is well represented by the Conference. General topology deals with the abstract properties of topological spaces; set-theoretic topology impinges upon the logical foundations of mathematics. The study of dynamical systems is close to Poincare's original motivation, and deals with the behavior of various iterative processes. These often give rise to complex objects, continua, which are studied in their own right. Geometric topology deals with manifolds, objects which are locally like n-dimensional Euclidean space, but whose global structure might be quite complicated. For instance, there is a lot of current activity in 3-dimensional topology, whose goal is essentially to describe all theoretically possible 3-dimensional universes. Rich connections have recently been discovered between this subject and quantum physics, while on the other hand topological techniques from the theory of knots in 3-dimensional space have recently been applied to the study of DNA. Finally, geometric group theory, a relatively new subject, studies groups, which are algebraic objects, from a topological point of view; this is leading to deep connections between topology and algebra. The interaction at the Conference between workers in all these different branches of topology is expected to be very fruitful.