Conference: CRM Thematic Program in Geometric Analysis

蒙特利尔数学研究中心(CRM)将于2024年4月15日至6月29日举办一个为期一学期的大型“几何分析主题课程”。该计划的科学活动将包括为期6周的专题研讨会、为期两周的暑期学校(高级数学研讨会)和两个艾森施塔特教席讲座。该计划的主要主题是几何分析。这是一个重要的数学领域，对数学和物理的许多其他部分有很大的影响和应用，它使用和发现分析和偏微分方程中的工具来解决源于几何和物理的问题。该计划将汇集几何分析不同方面的大量专家，并将吸引来自北美和其他地区的广泛和多样化的参与者。该计划的一个主要目标是让研究生和早期职业数学家了解这一重要数学领域的最新发展。这笔赠款将为美国的初级数学家(研究生和博士后)提供财政支持，特别是妇女和其他代表性不足群体的成员，通过帮助支付他们的旅费和住宿费。过去几年，在各种非常困难的几何问题上取得了惊人的进展，包括使用Ricci流的庞加莱猜想的壮观解，以及法诺流形的卡勒-爱因斯坦问题的解决。长期以来，非线性分析和几何之间的相互作用一直被证明是非常富有成效的。一般而言，涉及黎曼度量或Kahler度量的曲率张量的问题通常转化为非线性偏微分方程组，从分析的角度来看，这可能是一个巨大的挑战，但通常可以利用潜在的几何结构来攻击。6个专题讲习班的广泛主题将是：几何流动；复数和卡勒几何；6、7、8维的特殊几何；模空间和几何对象的奇点。短信暑期班的主题是“黎曼和复杂几何中的流动和变分方法：经典和现代方法”，并将由该领域的知名专家提供10个迷你课程。艾森施塔特主席将由西蒙·布伦德尔和帕纳乔塔·达斯卡洛普洛斯担任。主题计划网页可在此处找到：https://www.crmath.ca/en/activities/#/type/activity/id/3880This奖项反映了美国国家科学基金会的法定使命，通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The Centre de Recherches Mathematiques (CRM) in Montreal will host a large, semester-long "Thematic Program in Geometric Analysis" from April 15 to June 29, 2024. The scientific activities of this Program will consist of 6 week-long Thematic Workshops, a two-week long Summer School (Seminaire de Mathematiques Superieures SMS), and two Aisenstadt Chairs Lectures. The Program's main theme is Geometric Analysis. This is an important field of mathematics with great impact and applications to many other parts of mathematics and physics, which uses and discovers tools in analysis and partial differential equations to address problems which originate in geometry and physics. This Program will bring together a large number of experts in different facets of geometric analysis, and will attract a large and diverse spectrum of participants from North America and beyond. A major goal of this Program is to expose graduate students and early career mathematicians to the recent developments in this important field of mathematics. This grant will provide financial support for junior US-based mathematicians (graduate students and postdocs), particularly women and members of other under-represented groups, to participate in the Program, by helping cover their travel and lodging expenses.The last few years have seen spectacular progress on a variety of very difficult geometric problems, including the spectacular solution of the Poincare conjecture using Ricci Flow, and the solution of the Kahler-Einstein problem for Fano manifolds. The interplay between nonlinear analysis and geometry has long proved to be extremely fruitful. Generally speaking, problems involving the curvature tensor of a Riemannian or Kahler metric usually translate to nonlinear PDEs, which may present a formidable challenge from the analytic viewpoint, but which often can be attacked using the underlying geometric structure. The broad themes of the 6 Thematic Workshops will be: geometric flows; complex and Kahler geometry; special geometries in dimension 6,7,8; moduli spaces and singularities of geometric objects. The SMS summer school will be on "Flows and Variational Methods in Riemannian and Complex Geometry: Classical and Modern Methods", and will feature 10 mini-courses by well-known experts in the field. The Aisenstadt Chairs will be Simon Brendle and Panagiota Daskalopoulos.The Thematic Program webpage can be found here: https://www.crmath.ca/en/activities/#/type/activity/id/3880This 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.