Conference Proposal: Geometric Topology in Cortona

题为《科托纳的几何拓扑学：量子拓扑学与双曲几何的相互作用》的会议将于2013年6月3-8日在意大利科托纳举行。这次会议将聚焦于近年来有显著重叠的两个低维拓扑领域。特别是，会议将集中讨论双曲几何和量子拓扑之间的相互作用。在过去的二十年里，这两个领域都取得了重大进展。在双曲几何中，证明了关于三维流形及其覆盖的几何结构的几个长期存在的猜想。在量子方面，已经构造了一族TQFT，并证明它们与量子不变量有关，例如琼斯多项式。越来越多的证据表明，许多量子不变量与双曲几何有关，在这些方向上有几个公开的猜想，包括体积猜想及其变体。这次会议将汇集这两个领域的杰出国际研究人员。这次会议有三个中心目标。首先，它将把来自美国和其他国家的顶尖专家聚集在一起，讨论尖端研究，从而促进一个国际数学家小组之间的对话。第二，它将促进双曲几何学家和量子拓扑学家之间的思想交流和合作，导致这两个领域的进一步融合。最后，它将使研究生和早期职业数学家了解这些领域的重要发展。初级和高级数学家都将有机会了解新的研究，并向广大观众展示他们的结果。我们预计这将是一次重要的国际会议。欲了解更多信息，请访问会议网站：http://www.dm.unipi.it/~martelli/Cortona/Cortona.html.。

The conference entitled "Geometric Topology in Cortona: Interactions of quantum topology and hyperbolic geometry" will be held in Cortona, Italy, on June 3-8, 2013. This conference will focus on two areas of low-dimensional topology that have had significant overlap in recent years. In particular, the conference will concentrate on the interaction between hyperbolic geometry and quantum topology. In the last two decades, both of these areas have seen significant progress. In hyperbolic geometry, several longstanding conjectures concerning the geometric structure of 3-manifolds and their covers have been proved. On the quantum side, families of TQFTs have been constructed and shown to be related to quantum invariants such as the Jones polynomial. There is increasing evidence that many quantum invariants have connections to hyperbolic geometry, and there are several open conjectures in these directions, including the Volume Conjecture and its variants. This conference will bring together outstanding international researchers in both fields.This conference has three central goals. First, it will stimulate dialogue among an international group of mathematicians, by bringing together leading experts from the US and other countries to discuss cutting edge research. Second, it will promote an exchange of ideas and collaboration among hyperbolic geometers and quantum topologists, leading to further integration of these two fields. Finally, it will expose graduate students and early career mathematicians to the important developments in these areas. Both junior and senior mathematicians will be given an opportunity to learn of new research and present their results to a broad audience. We expect that this will be a major international conference. More information is available on the conference website: http://www.dm.unipi.it/~martelli/Cortona/Cortona.html.