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“科尔托纳的几何拓扑：量子拓扑和双曲几何的相互作用”的会议将于2013年6月3日至8日在意大利科尔托纳举行。 本次会议将重点讨论近年来有重大重叠的两个低维拓扑领域。 特别是，会议将集中在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，关于三维流形及其覆盖的几何结构的几个由来已久的命题已经被证明。 在量子方面，TQFT家族已经被构建，并被证明与量子不变量（如琼斯多项式）有关。 越来越多的证据表明，许多量子不变量与双曲几何有联系，在这些方向上有几个开放的猜想，包括体积猜想及其变体。 这次会议将汇集这两个领域的优秀国际研究人员。 首先，它将通过汇集来自美国和其他国家的顶尖专家来讨论前沿研究，促进国际数学家团体之间的对话。 其次，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，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到这些领域的重要发展。 初级和高级数学家将有机会了解新的研究，并向广大观众展示他们的成果。 我们预计这将是一次重要的国际会议。更多信息请访问会议网站：http://www.dm.unipi.it/~martelli/Cortona/Cortona.html。