Frontiers in Geometry Conference 2022

2022 年几何前沿会议

• 批准号: 2154823
• 负责人: Paul Feehan
• 金额: $ 3.84万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2154823&HistoricalAwards=false
• 关键词: Frontiers; Geometry; Conference; 2022

The Frontiers in Geometry Conference will take place during the period August 1-12, 2022, at the Abdus Salam International Center for Theoretical Physics (ICTP), Trieste, Italy. The conference is a two-week activity (a one-week graduate summer school, followed by a one-week conference) that is co-organized by Paul Feehan (Rutgers University), Lenhard Ng (Duke University), Peter Ozsváth (Princeton University), Yongbin Ruan (Zhejiang University), and Paul Seidel (MIT). Claudio Arezzo, Acting Head of the Mathematics Section, ICTP, is the local meeting co-organizer. The scientific themes of the event include low-dimensional and symplectic topology, knot theory, and analytical aspects of gauge theory. The summer school is led by five eminent early-career mathematicians and the conference features twenty-five well-known mathematicians, all leading scientists. The conference website links to that of the graduate summer school and will be developed and maintained by ICTP: http://indico.ictp.it/event/9706There has been exciting recent progress in low-dimensional and symplectic topology, spurred by the growing understanding of Floer homologies and Khovanov homology. Moreover, there is promise of entirely new invariants and methods, which arise out of progress in the analytical aspects of gauge theory (new compactness theorems and higher-dimensional gauge-theoretic equations) and of pseudo-holomorphic curves. For example, there is an ongoing effort to use the Kapustin-Witten equations to extract a more intrinsically geometric definition of the Jones polynomial and Khovanov homology and, eventually, new generalizations of those invariants. Gains in the understanding of any one of these topics will enrich the understanding of all. The proposed meeting will bring together experts at the frontier of research in these topics from around the world. The conference is expected to generate transfers of knowledge, new collaborations, and a cross-fertilization of ideas, and further inspire graduate students and early-career mathematicians. Because of the location of ICTP within a geographic concentration of leading European mathematics departments and near good public transportation facilities and because of ICTP's commitment to hosting mathematicians from developing countries as well, the U.S.-based participants will have the opportunity to interact with a distinguished and diverse group of mathematical leaders and rising stars. The meeting will thus help to support, train and encourage the next generation of researchers and strengthen international connections among them.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

几何前沿会议将于2022年8月1日至12日在意大利的里雅斯特的Abdus Salam国际理论物理中心（ICTP）举行。会议是由Paul Feehan（罗格斯大学），Lenhard Ng（杜克大学），Peter Ozsváth（普林斯顿大学），Yongbin阮永斌（浙江大学）和Paul Seidel（麻省理工学院）共同组织的为期两周的活动（一周的研究生暑期学校，随后是一周的会议）。Claudio Arezzo， ICTP数学科代理主任，是当地会议的共同组织者。本次活动的科学主题包括低维和辛拓扑，结理论和规范理论的分析方面。暑期学校由五位杰出的早期职业数学家领导，会议有25位知名数学家，都是顶尖的科学家。会议网站链接到研究生暑期学校的网站，将由ICTP开发和维护：http://indico.ictp.it/event/9706There最近在低维和辛拓扑方面取得了令人兴奋的进展，这是由对Floer同调和Khovanov同调的日益了解所推动的。此外，由于规范论（新的紧性定理和高维规范论方程）和伪全纯曲线的分析方面的进展，有可能出现全新的不变量和方法。例如，目前正在努力使用Kapustin-Witten方程来提取Jones多项式和Khovanov同调的更本质的几何定义，并最终得到这些不变量的新推广。在理解这些主题中的任何一个方面取得的进展都将丰富对所有主题的理解。这次会议将汇集来自世界各地这些主题研究前沿的专家。这次会议有望产生知识的转移、新的合作和思想的交流，并进一步激励研究生和早期职业数学家。由于ICTP的地理位置集中在欧洲领先的数学系，靠近良好的公共交通设施，并且由于ICTP承诺接待来自发展中国家的数学家，美国的参与者将有机会与杰出的、多样化的数学领袖和新星群体进行互动。因此，会议将有助于支持、培训和鼓励下一代研究人员，并加强他们之间的国际联系。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。