Conference: Geometric flows and applications

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日在英国爱丁堡的ICMS贝叶斯中心举行。该活动将汇集几何和拓扑学方面的研究人员，他们的研究兴趣与几何流已经或有望发挥关键作用的主题密切相关，并将包括几何流分析方面的专家。具体的主题将包括复杂几何，厄米几何，辛和接触拓扑，特殊完整，校准几何和规范理论，以及黎曼几何和低维拓扑。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。杰出的知名演讲者将吸引来自美国各地的年轻参与者。通过邀请有前途的年轻人参加，一些有贡献的演讲，这次会议将有助于培养和支持该领域未来的领导者。预计这次会议将产生新的合作和研究论文。本次会议的主题是几何流的研究及其在几何和拓扑学中不同主题的应用。几何流是解决几何和拓扑等不同领域重要问题的强大工具。惊人的成功至少可以追溯到唐纳森对希钦-小林通信的研究，并继续到现在，证明了庞加莱猜想和几何化猜想、可微球定理和广义小猜想。在一系列领域中，几何流动提供了一种自然的方法，而其他方法迄今证明是不成功的，仍然有许多具有根本重要性的关键开放问题。几何流是非线性的，抛物线演化方程的关键几何量，这是一个丰富的和发展的理论的核心，结合了偏微分方程和微分几何的研究。这些流中最著名的例子是Ricci流和平均曲率流，它们都有重要的应用，特别是在拓扑学中。通过使用流形上的附加数据（例如，一个复杂的结构），可以定义几何流，现在可以用来研究这些更精细的几何。这被证明是非常富有成效的，例如在测量理论的应用（潜在的和已经实现的），最小模型程序的研究以及复杂几何和代数几何、辛拓扑、镜像对称和例外完整学中的相关问题。会议的网站是：https://www.icms.org.uk/workshops/2023/geometric-flows-and-applicationsThis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。

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.