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

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AbstractAward: DMS-0603270Principal Investigator: Marc E. Culler, Steven BoyerThe subject of 3-manifold topology has a long history of deep andinteresting interactions with other parts of mathematics. Thecomplexity of these connections has increased with time, as thesubject developed, and it has exploded in recent years. Thecoincidence of this explosion with the recent solution of severalof the major outstanding problems in the area make this a goodtime for reflection on its relationship to the rest ofmathematics. This grant will support participants in aconference, to be held at CRM in Montreal, which aims to bringtogether a varied group of leading researchers whose workdemonstrates deep connections between 3-manifold topology andother areas of mathematics. The speakers will include leadingresearchers in areas such as: geometrization of 3-manifolds;combinatorial group theory and coarse geometric properties ofgroups; properties of random 3-manifolds and asymptoticproperties of hyperbolic surfaces; Floer homology,Khovanov-Rozansky homology; 3-manifold invariants arising fromcontact structures; character varieties; and Dehn surgery. Theconference will honor Peter Shalen, whose work has been a majorforce in bringing many different aspect of mathematics to bear onthe study of 3-manifolds, and in expanding the influence of3-manifold topology into other areas.Throughout history the interaction between mathematics andscience has been characterized by the mysterious phenomenon thatmathematical ideas which are developed with no specificapplication in mind turn out to be perfectly suited for futureapplications to science. For example, differential geometry,which provided the ideal mathematical foundation for Einstein'sgeneral relativity theory, was developed much earlier bymathematicians who could not have anticipated the way in which itwould be applied in physics. On a smaller scale, there is asimilar phenomenon involving different areas of mathematics. Arecent example of this, which is directly related to the topic ofthis conference, is provided by Perelman's proof of Thurston'sGeometrization Conjecture. This conference aims to facilitatethese sorts of unexpected fruitful interactions between differentareas of mathematics. The central topic of the conference is thestudy of 3-dimensional spaces. Speakers have been selected whosework involves significant new applications to this subject ofideas which originate from a wide range of other areas ofmathematics.The conference web site ishttp://www.crm.umontreal.ca/cal/fr/mois200606.html.