Conference: Geometric flows and applications

会议：几何流及应用

• 批准号: 2316597
• 负责人: Natasa Sesum
• 金额: $ 1.1万
• 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: 2023
• 资助国家: 美国
• 起止时间: 2023-07-15 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2316597&HistoricalAwards=false
• 关键词: Conference; Geometric; flows; applications

The award will support US participants attending the conference 'Geometric Flows and Applications', which will take place on July 10-14th at ICMS, Bayes Center in Edinburgh, UK. The event will bring together researchers in geometry and topology whose research interests are closely aligned to topics where geometric flows either already or are expected to play a key role, and will include experts in the analysis of geometric flows. Specific topics will include aspects of complex geometry, Hermitian geometry, symplectic and contact topology, special holonomy, calibrated geometry and gauge theory, as well as Riemannian geometry and low-dimensional topology. A major goal of this conference is to support, train and encourage the next generation of mathematicians in the fields of analysis, complex geometry and mathematical physics. The distinguished and well-known speakers will draw in junior participants from all over the US. By inviting promising junior people to attend, some contributing talks, this conference will help to nurture and support the future leaders of the field. New collaborations and research papers are expected to emerge from this meeting. The theme of this conference is the study of geometric flows and their applications to diverse topics in geometry and topology. Geometric flows are powerful tools for tackling important problems across diverse areas in geometry and topology, and beyond. Spectacular successes go back at least to Donaldson’s work on the Hitchin–Kobayashi correspondence, and continue to the present, with the proofs of the Poincar\'e and Geometrization Conjectures, the Differentiable Sphere Theorem, and the Generalized Smale Conjecture. There are still many key open problems of fundamental importance in a range of areas for which geometric flows provide a natural approach, and for which other methods have proved unsuccessful thus far. Geometric flows are nonlinear, parabolic evolution equations for key geometric quantities, which lie at the heart of a rich and developing theory combining the study of partial differential equations and differential geometry. The most well-known examples of these flows are the Ricci flow and the mean curvature flow, both of which have significant applications, particularly to topology. By using additional data on the manifold (for example, a complex structure), one can define geometric flows which now can now be used to study these more refined geometries. This has proved extremely fruitful, for example in applications (both potential and realised) to gauge theory, the study of the minimal model programme and related problems in complex and algebraic geometry, symplectic topology, Mirror Symmetry and exceptional holonomy. The website for the conference is: https://www.icms.org.uk/workshops/2023/geometric-flows-and-applicationsThis 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.

该奖项将支持参加“几何流与应用”会议的美国参与者，该会议将于 7 月 10 日至 14 日在英国爱丁堡贝叶斯中心 ICMS 举行。该活动将汇集研究兴趣密切的几何和拓扑研究人员。与几何流已经或预计发挥关键作用的主题保持一致，并将包括几何流分析方面的专家。具体主题将包括复杂几何、埃尔米特几何、辛和接触拓扑、特殊几何等方面。本次会议的一个主要目标是支持、培训和鼓励分析、复杂几何和数学物理领域的下一代数学家。知名演讲者将吸引来自美国各地的青年参与者，通过邀请有前途的青年人参加一些有贡献的演讲，本次会议将有助于培养和支持该领域的未来领导者。从中脱颖而出本次会议的主题是几何流及其在几何和拓扑中不同主题中的应用，几何流是解决几何和拓扑等不同领域的重要问题的强大工具。唐纳森关于希钦-小林对应的工作，并延续至今，证明了庞加莱猜想和几何化猜想、可微球定理和广义小林猜想。在一系列领域中仍然存在许多具有根本重要性的关键开放问题，几何流为这些问题提供了自然的方法，而迄今为止其他方法已被证明是不成功的关键几何量的非线性抛物线演化方程，它是结合偏微分方程和微分几何研究的丰富且不断发展的理论的核心。这些流最著名的例子是里奇流和平均曲率流，两者都有重要的应用，特别是在应用领域。通过使用额外的拓扑。通过流形上的数据（例如，复杂的结构），人们可以定义几何流，现在可以使用几何流来研究这些更精细的几何形状，这已被证明是非常富有成效的，例如在规范理论的应用（潜在的和已实现的）中。 ，研究复杂代数几何、辛拓扑、镜像对称和例外完整学中的最小模型程序和相关问题。会议网站是： https://www.icms.org.uk/workshops/2023/geometric-flows-and-applications 该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。