A Workshop and Conference is being held at the University of Melbourne, Australia, to bring together active, leading, international experts and emerging researchers to report on recent results and explore future directions in the field of Geometry and Topology. Particular emphasis will be placed on one of its most active branches, the study of 3-manifolds. Geometric structures on 3-manifolds are known to exist by Perelman's work on the Ricci flow, but relatively little is known about the interplay between analysis and geometry, and how to construct geometric structures directly. The Workshop will be targeted at early career researchers and will feature short courses covering a broad range of materials and techniques being used at the frontier of research in dynamical and probabilistic methods in geometric group theory, invariants of hyperbolic 3-manifolds, and new methods in distinguishing knots and links. The Conference will highlight ongoing research focused on finding direct connections between analysis, geometry, and topology of 3-manifolds.

This project will enable Early Research Career mathematicians from the United States to attend a Workshop and Conference at the University of Melbourne, Australia, on recent results and new directions in the geometry and topology of 3-manifolds. This is one of the most active and rapidly changing areas of mathematical research. Participation will give these young researchers access to short courses on new results and techniques for future research and bring them together with leading international experts in the area. The Workshop and Conference will have broad appeal to group theorists, analysts, differential geometers, and low-dimensional topologists. It will bring about interaction between emerging researchers and experts and expose the potential for future collaborations.

Project Report

This two-week Workshop and Conference consisted of an introductory week of expository lecturers followed by a week of research presentations by leading experts in geometry and topology. The event brought together 115 graduate students and researchers from the United States, Europe, Asia and Australia. The Workshop (July 11-15, 2011) and Conference (July 18-22, 2011) covered a broad range of topics in geometry and topology, including hyperbolic and symplectic geometry, Heegaard splittings, triangulations of 3-maifolds, geometric group theory, and recent results on graph manifolds. The event was designed so that it was beneficial not only to the experts in the field but also to early career researchers and graduate students. During the conference there were 23 international experts who reported on a variety of new results. For instance, proof of an outstanding conjecture, recent progress across many areas, new directions in research, and new computational techniques. Each day there was a short expository talk on a concept or procedure relevant to a better understanding of the principal areas of the conference. The talks were positively received by both junior and senior researchers. The workshop and conference proceedings includes 17 peer reviewed expository and research articles and is published by the American Mathematical Society as Geometry & Topology Down Under: A Conference in Honour of Hyam Rubinstein.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Christopher W. Stark
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Oklahoma State University
United States
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