Conference: Gauge Theory and Topology

会议：规范理论与拓扑

• 批准号: 2308798
• 负责人: Olga Plamenevskaya
• 金额: $ 4万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-06-01 至 2024-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2308798&HistoricalAwards=false
• 关键词: Conference; Gauge; Theory; Topology

This awards support participation of US-based mathematicians in the conference "Gauge Theory and Topology", which will take place at the Clay Mathematics Institute, Oxford, UK, on July 24-28, 2023.The conference will bring experts from around the world together to discuss issues of current interest in geometry and topology, focusing on the areas of Floer homology, low-dimensional topology, and gauge theory. A broad range of topics within the field will be covered, creating opportunities for interaction of researchers at different career stages and those working in different subfields. The breadth of conference topics will present an excellent training opportunity for young researchers, who would be exposed to a wealth of current knowledge and a range of long-standing and newly accessible problems in the field. The funding will primarily be used to support graduate students and young researchers, with priority given to qualified participants from underrepresented groups.Beginning with the discovery of Donaldson theory, Seiberg-Witten theory, and Floer homology several decades ago, extracting geometrical and topological meaning from equations on manifolds has been a powerful tool that led to many breakthroughs in the area, often in combination with the more classical topological techniques. These areas of mathematics, as well as newer subfields such as Heegaard Floer theory, continue to thrive, but each has grown to become a separate field, with somewhat limited interaction between them. The meeting will encompass a broad range of topics to encourage cross-fertilization of ideas and connections and collaborations of experts in different subfields. Topics of particular current interest include new developments in gauge theory and geometric partial differential equations, including instanton invariants and the family Seiberg-Witten invariants; the topology of 4-manifolds, including advances in topological 4-manifolds and the study of embedded surfaces; and Floer homology for 3-manifolds, including equivariant Floer homology, knot detection and the relations between instanton and monopole homology. The conference will focus on recent achievements and new developments in gauge theory and topology. It is expected to give rise to new questions, opening the door to further progress in the area.Webpage: https://www.claymath.org/events/gauge-theory-and-topology-celebration-peter-kronheimers-60th-birthdayThis 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.

该奖项支持美国数学家参加将于2023年7月24日至28日在英国牛津大学克莱数学研究所举行的“规范理论和拓扑”会议。该会议将汇集来自世界各地的专家，讨论几何和拓扑学中当前感兴趣的问题，重点关注Floer同调，低维拓扑和规范理论领域。将涵盖该领域内的广泛主题，为不同职业阶段的研究人员和在不同子领域工作的研究人员创造互动机会。 会议主题的广度将为年轻的研究人员提供一个极好的培训机会，他们将接触到丰富的当前知识以及该领域的一系列长期和新问题。从几十年前发现唐纳森理论、Seiberg-Witten理论和Floer同调开始，从流形上的方程中提取几何和拓扑意义一直是一个强大的工具，导致了该领域的许多突破，通常与更经典的拓扑技术相结合。这些数学领域，以及较新的子领域，如Heegaard Floer理论，继续蓬勃发展，但每一个都已经发展成为一个独立的领域，它们之间的相互作用有些有限。会议将涵盖广泛的主题，以鼓励不同分领域的专家相互交流思想、建立联系和开展合作。当前特别感兴趣的主题包括规范理论和几何偏微分方程的新发展，包括瞬子不变量和Seiberg-Witten不变量; 4-流形的拓扑，包括拓扑4-流形的进展和嵌入表面的研究;和3-流形的Floer同调，包括等变Floer同调，结检测和瞬子与非瞬子同调之间的关系。会议将集中讨论规范理论和拓扑学的最新成就和新发展。https://www.claymath.org/events/gauge-theory-and-topology-celebration-peter-kronheimers-60th-birthdayThis奖项反映了NSF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。