William Rowan Hamilton Geometry and Topology Workshop

第六届William Rowan哈密尔顿几何和拓扑研讨会是一个为期三天的关于纽结、曲面和三流形的指导研讨会，将于2010年9月2日至4日在爱尔兰都柏林的汉密尔顿数学研究所(HMI)举行。威廉·罗文·哈密尔顿几何和拓扑学研讨会的目的是调查当前几何和拓扑学研究的重要领域中的共同主题和技术，并支持对这些领域感兴趣的初级研究人员。今年的工作坊将汇集几何和拓扑学领域的顶尖研究人员，他们对与纽结、曲面和三流形相关的问题特别感兴趣，并将研究这些领域研究前沿的一些重要问题。来自不同领域的专业知识的汇聚将导致新的合作项目，并拓宽参与者的研究视野。研讨会的主要议题之一将是虚拟哈肯猜想，即每个封闭的双曲3-流形都有一个有限覆盖，其中包含一个封闭的不可压缩曲面。近年来，这个猜想激发了许多研究人员的广泛工作，也是该领域的主要问题之一。新的和令人兴奋的想法的涌现，特别是Kahn和Markovic对表面子群猜想的证明，Wise关于拟凸层次结构的工作，以及Agol的虚拟纤维准则，为解决这个问题提供了新的途径，有理由相信解决方案可能即将到来。研讨会还将集中介绍Heegaard Floer理论研究人员在低维拓扑学方面取得的最新进展。我们将讨论这一领域的公开问题，包括Berge猜想，它给出了三个球面中允许进行透镜空间手术的结的猜想列表。另一个话题将是Guilfoyle和Klingenberg最近宣布的Caratheodory猜想的证明，即三维欧氏空间中的任何闭凸曲面必至少有2个脐点。通过分享新的技术和见解，希望能够在这些重要问题上取得进展。

The sixth William Rowan Hamilton Geometry and Topology Workshop is a three-day, directed workshop on Knots, Surfaces and Three-Manifolds, to be held at the Hamilton Mathematical Institute (HMI) in Dublin, Ireland September 2-4, 2010. The purpose of the William Rowan Hamilton Geometry and Topology Workshop is to investigate common themes and techniques among significant areas of current research in geometry and topology and to support junior researchers interested in these areas. This years workshop will bring together leading researchers in geometry and topology who have a special interest in problems related to Knots, Surfaces and Three-Manifolds and will investigate a number of important questions at the forefront of research in these areas. The confluence of expertise from different areas will result in new collaborative projects, and in broadening the research horizons of the participants. Among the main topics of the workshop will be the virtual Haken conjecture, that every closed hyperbolic 3-manifold has a finite cover that contains a closed incompressible surface. The conjecture has motivated extensive work of many researchers in recent times, and is one of the main problems in the area. A surge of new and exciting ideas, in particular Kahn and Markovic's proof of the surface subgroup conjecture, Wise's work on quasiconvex heirarchies, and Agol's virtual fibering criterion, has provided new avenues to tackle this problem and there is reason to believe that a solution may well be in sight. The workshop will also concentrate on recent advances in low-dimensional topology made by researchers in Heegaard Floer theory. We will discuss open questions in the field including the Berge conjecture which gives a conjectural list of those knots in the three-sphere which admit a Lens-space surgery. Another topic will be the recently announced proof by Guilfoyle and Klingenberg of the Caratheodory conjecture, that any closed convex surface in 3-dimensional Euclidean space must have at least 2 umbilic points. Through sharing new techniques and insights, it is hoped that progress can be made on a number of these important questions.