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.

该奖项为将于2022年6月13日至17日在西雅图举行的“共形几何，分析和物理”会议提供支持。在过去的三十年里，共形几何领域与几何分析和物理学，特别是高能物理和凝聚态物理有着丰富的相互作用。在这两种情况下的好处是双向的：保形几何导致了新的分析工具的发展注入几何直观，这反过来又导致解决重要的几何问题。同样，物理学是新问题和重要见解的来源，而保形几何提供了解决物理问题的关键工具。本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。预计会议将促进所有三个领域的进一步发展和跨越多种边界的合作。促进早期职业研究人员进入与所有三个领域的对话是本次活动的一个特殊目标。共形几何是定义了角而不是长度的空间几何。它在物理学中有着长期的、最近快速增长的相关性，它是一种工具，为许多旧现象提供了新的视角。相反，物理学一直是共形几何的见解和问题的丰富来源。多年来，共形几何本身提供了一些最引人注目的问题，在几何分析，而技术，散射理论和偏微分方程已经使该领域的巨大进步。会议的主要目标是将工作重叠的三个标题领域的研究人员聚集在一起，以传播进展，分享有趣的问题，建立关系并拓宽视野。会议将允许接触到相关的国家的最先进的技术，在共形几何，分析和物理与其他感兴趣的从业者在每个领域分享。它将促进美国和其他国家之间的国际合作，以及数学家和物理学家之间的合作。初级参与者将获得有价值的见解，以及与更高级从业者的关系，这可能会塑造他们的职业生涯和他们的数学（或物理）观点。他们将有机会展示自己的工作，各级研究人员之间将有合作机会。大部分资金将用于支持初级数学家。将作出巨大努力，招聘妇女和其他数学领域代表性不足的群体的成员。https://personal.utdallas.edu/~sxm190098/graham65/该奖项反映了NSF的法定使命，并被认为值得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来支持。