Conformal Geometry, Analysis, and Physics

共形几何、分析和物理

• 批准号: 2154127
• 负责人: Gunther Uhlmann
• 金额: $ 4.5万
• 依托单位: University of Washington
• 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: 2022-06-01 至 2023-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2154127&HistoricalAwards=false
• 关键词: Conformal; Geometry; Analysis; Physics

This award provides support for the conference "Conformal Geometry, Analysis, and Physics" to be held in Seattle from June 13-17, 2022. The field of conformal geometry has had rich interactions with both geometric analysis and physics, especially high-energy and condensed-matter physics, over the past three decades. The benefits have been bidirectional in both cases: conformal geometry has led to the development of new analytic tools infused by geometric intuitions, which in turn lead to the solution of important geometric problems. Similarly, physics is a source both of new problems and of important insights, while conformal geometry provides crucial tools in the solution of physical problems. This conference will bring together experts from all of these fields to share and discuss their research and benefit from each other's perspectives and tools. It is expected that the conference will stimulate further development in all three fields and cooperation across many kinds of boundaries. Facilitating entry of early-career researchers into dialog with all three areas is a particular goal for this event. A poster session will be held for students.Conformal geometry is the geometry of spaces where angles are defined, but not lengths. It has had a long and, recently, fast-growing relevance in physics, where it is a tool that provides new perspectives on many old phenomena. Conversely, physics has been a rich source of insights and problems in conformal geometry. For many years now, conformal geometry itself has provided some of the most compelling problems in geometric analysis, while techniques from analysis, scattering theory, and partial differential equations have enabled tremendous progress in the field. The primary goal of the conference is to bring together researchers from the three title areas whose work overlaps, in order to disseminate progress, share interesting problems, build relationships, and broaden perspectives. The conference will allow exposure to relevant state-of-the-art techniques in conformal geometry, analysis, and physics to be shared with other interested practitioners in each field. It will foster international collaboration between the US and other countries, and also collaboration between mathematicians and physicists. Junior participants will gain valuable insights, and relationships with more senior practitioners that may shape both their career and their mathematical (or physical) perspectives. Opportunity will be given for them to present their own work, and collaboration opportunities will exist between researchers at all levels. Most of the funding will be used to support junior mathematicians. Substantial effort will be made in recruiting women and members of other underrepresented groups in mathematics. The conference website is at https://personal.utdallas.edu/~sxm190098/graham65/ .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.

该奖项提供了对2022年6月13日至17日在西雅图举行的“共形几何学，分析和物理学”的支持。保形几何领域与几何分析和物理学，尤其是高能和高能和物理学都有丰富的相互作用在过去的三十年中，凝结的物理学。在这两种情况下，好处都是双向的：保形几何形状导致了由几何直觉注入的新分析工具的开发，进而导致解决重要的几何问题的解决方案。同样，物理学既是新问题和重要见解的来源，而保形几何形状为解决物理问题的解决方案提供了重要的工具。这次会议将汇集来自所有这些领域的专家，分享和讨论他们的研究并从彼此的观点和工具中受益。预计会议将刺激所有三个领域的进一步发展，并在许多界限上进行合作。促进早期研究人员进入与所有三个领域的对话是一个特殊的目标。将为学生举行海报会话。符合形状的几何形状是定义角度但不长度的空间的几何形状。它在物理学中具有漫长而又快速增长的相关性，它是一种为许多旧现象提供新观点的工具。相反，物理学一直是保形几何学的洞察力和问题的丰富来源。多年以来，保形几何本身在几何分析中提供了一些最引人注目的问题，而分析，散射理论和部分微分方程的技术已在该领域取得了巨大进步。会议的主要目标是将研究人员从三个标题领域的研究人员汇集在一起​​，这些领域的工作重叠，以传播进步，共享有趣的问题，建立关系和拓宽观点。该会议将允许与每个领域的其他有兴趣的从业人员共享保形几何，分析和物理学中相关的最新技术。它将促进美国与其他国家之间的国际合作，以及数学家与物理学家之间的合作。初级参与者将获得宝贵的见解，并与更多的高级从业人员的关系，这些从业人员可能会塑造他们的职业和数学（或物理）观点。他们将有机会展示自己的作品，并且在各级研究人员之间将存在协作机会。大多数资金将用于支持初级数学家。将在招募妇女和其他代表性不足的数学群体的成员方面做出巨大的努力。会议网站位于https://personal.utdallas.edu/~sxm190098/graham65/。这项奖项反映了NSF的法定任务，并被认为值得通过基金会的知识分子优点和更广泛的影响标准通过评估来进行评估。