Conference Proposal: Geometric Topology in Cortona

会议提案：科尔托纳的几何拓扑

• 批准号: 1313541
• 负责人: David Futer
• 金额: $ 4.5万
• 依托单位: Temple University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-05-01 至 2014-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1313541&HistoricalAwards=false
• 关键词: Conference; Proposal; Geometric; Topology; Cortona

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.

题为“ Cortona的几何拓扑：量子拓扑与双曲线几何形状的相互作用”的会议将于2013年6月3日至8日在意大利科尔托纳举行。近年来，该会议将重点关注两个低维拓扑的领域。 特别是，该会议将集中于双曲几何形状和量子拓扑之间的相互作用。在过去的二十年中，这两个领域都取得了重大进展。 在双曲线几何形状中，已经证明了几种关于3型脉冲及其覆盖的几何结构的长期猜想。 在量子方面，已经构建了TQFT的家族并显示与诸如琼斯多项式等量子不变性有关。 越来越多的证据表明，许多量子不变性与双曲线几何形状有连接，并且这些方向上有几个开放猜想，包括体积猜想及其变体。 这次会议将在这两个领域中汇集杰出的国际研究人员。这次会议有三个中心目标。 首先，它将通过将来自美国和其他国家的主要专家汇聚在一起讨论尖端研究，从而刺激国际数学家群体之间的对话。 其次，它将促进双曲线几何学和量子拓扑师之间的思想和协作交流，从而进一步整合这两个领域。 最后，它将使研究生和早期职业数学家接触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，并向广泛的受众介绍他们的结果。 我们预计这将是一次主要的国际会议。会议网站上提供更多信息：http：//www.dm.unipi.it/~martelli/cortona/cortona/cortona.html。