3-Manifolds After Perelman; March 2006; Edinburgh, UK

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AbstractAward: DMS-0601251Principal Investigator: Cameron McA. Gordon, Alan W. ReidThe project is a workshop on 3-dimensional topology that will be held atthe International Centre for Mathematical Sciences in Edinburgh, UK, inMarch, 2006. Thurston's Geometrization Conjecture, which has guidedresearch in 3-dimensional topology for almost three decades, has nowbeen established, and consequently there is a need to set out a programfor future research in the subject. This is the objective of theworkshop. The program will be centered around five series of three1-hour lectures, given by Jeff Brock, Dave Gabai, Marc Lackenby, PeterOzsvath, and Peter Shalen. There will also be nine additional invited1-hour talks by other leading researchers. Among the recent importantdevelopments in 3-dimensional topology that will be discussed, with aview to illuminating the theory of 3-manifolds beyond Geometrization,are: the proofs of the Tameness and Ending Lamination Conjectures,Heegaard Floer homology theory, various approaches to the virtual HakenConjecture, and the connection between 3-dimensional topology and thetheory of word hyperbolic groups.3-dimensional topology is a large and active subject within the generalfield of pure mathematics. Its goal is the study of all possible3-dimensional "spaces", and of the various objects that can be situatedin them, such as knots. Over the last 30 years or so this subject hasseen many exciting developments, revealing connections to many otherbranches of mathematics as well as quantum physics and (in the case ofknots) even to the behavior of DNA. The guiding light of the subjectduring this period has been the Geometrization Conjecture, put forwardWilliam Thurston in the mid 1970's, which asserts that hyperbolicgeometry, the non-euclidean geometry discovered by Lobachevsky in the19th century, plays a key role in the description of these 3-dimensionalspaces. This conjecture was recently proved by Grisha Perelman. It seemstimely, then, to take stock of the subject, identifying the majorproblems that remain and indicating potential techniques and directionsfor future work. The core of the program will be five series of three1-hour lectures, given by five internationally renowned experts in thesubject. It is expected that this will make the workshop especiallyuseful to young researchers.The conference web site ishttp://www.icms.org.uk/meetings/2006/3-manifolds/index.html.