Journees Peter Shalen - A Conference on 3-Dimensional Topology and Its Role in Mathematics

University Of Illinois At Chicago, Chicago IL

Investigators

Abstract

Abstract Award: DMS-0603270 Principal Investigator: Marc E. Culler, Steven Boyer The subject of 3-manifold topology has a long history of deep and interesting interactions with other parts of mathematics. The complexity of these connections has increased with time, as the subject developed, and it has exploded in recent years. The coincidence of this explosion with the recent solution of several of the major outstanding problems in the area make this a good time for reflection on its relationship to the rest of mathematics. This grant will support participants in a conference, to be held at CRM in Montreal, which aims to bring together a varied group of leading researchers whose work demonstrates deep connections between 3-manifold topology and other areas of mathematics. The speakers will include leading researchers in areas such as: geometrization of 3-manifolds; combinatorial group theory and coarse geometric properties of groups; properties of random 3-manifolds and asymptotic properties of hyperbolic surfaces; Floer homology, Khovanov-Rozansky homology; 3-manifold invariants arising from contact structures; character varieties; and Dehn surgery. The conference will honor Peter Shalen, whose work has been a major force in bringing many different aspect of mathematics to bear on the study of 3-manifolds, and in expanding the influence of 3-manifold topology into other areas. Throughout history the interaction between mathematics and science has been characterized by the mysterious phenomenon that mathematical ideas which are developed with no specific application in mind turn out to be perfectly suited for future applications to science. For example, differential geometry, which provided the ideal mathematical foundation for Einstein's general relativity theory, was developed much earlier by mathematicians who could not have anticipated the way in which it would be applied in physics. On a smaller scale, there is a similar phenomenon involving different areas of mathematics. A recent example of this, which is directly related to the topic of this conference, is provided by Perelman's proof of Thurston's Geometrization Conjecture. This conference aims to facilitate these sorts of unexpected fruitful interactions between different areas of mathematics. The central topic of the conference is the study of 3-dimensional spaces. Speakers have been selected whose work involves significant new applications to this subject of ideas which originate from a wide range of other areas of mathematics. The conference web site is http://www.crm.umontreal.ca/cal/fr/mois200606.html.