Geometry and Topology Down Under

Oklahoma State University, Stillwater OK

Investigators

Abstract

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.