Conference: Gauge Theory and Topology

该奖项支持美国数学家参加“规范理论与拓扑”会议，该会议将于2023年7月24日至28日在英国牛津克莱数学研究所举行。会议将汇集来自世界各地的专家，讨论当前对几何和拓扑感兴趣的问题，重点是弗洛尔同调、低维拓扑和规范理论等领域。该领域将涵盖广泛的主题，为不同职业阶段和不同子领域的研究人员创造互动的机会。会议议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和该领域一系列长期存在的和新的问题。这笔资金将主要用于支持研究生和年轻研究人员，优先考虑来自代表性不足群体的合格参与者。从几十年前Donaldson理论、Seiberg-Witten理论和Floer同构的发现开始，从流形上的方程中提取几何和拓扑意义已经成为一种强大的工具，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 flower理论，继续蓬勃发展，但每个领域都已发展成为一个独立的领域，它们之间的互动有限。会议将涵盖广泛的主题，以鼓励不同子领域的专家之间的思想交流、联系和合作。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，包括瞬时不变量和Seiberg-Witten不变量族；4-流形的拓扑结构，包括拓扑4-流形的研究进展和嵌入式表面的研究进展；3流形的花同源性，包括等变花同源性、结检测以及瞬子与单极子同源性的关系。会议将集中讨论规范理论和拓扑学的最新成就和新发展。预计它将引发新的问题，为该领域的进一步进展打开大门。网页：https://www.claymath.org/events/gauge-theory-and-topology-celebration-peter-kronheimers-60th-birthdayThis该奖项反映了美国国家科学基金会的法定使命，并通过基金会的知识价值和更广泛的影响审查标准进行评估，认为值得支持。

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.