Conference on Special Metrics in Complex Geometry

复几何特殊度量大会将于2021年1月7日至10日在佛罗里达国际大学举行。复流形是使用复数定义的高维曲面。最近，在复杂流形上的“度量”的研究取得了重大进展，复杂流形上的对象赋予这些空间一个形状，或者更准确地说，曲率。对这些指标的研究是复杂几何和几何分析的结合点。这次会议的目的是将这两个领域的专家聚集在一起，讨论这些令人兴奋的新发展。尽管最近有许多关于复杂几何的会议，但没有一次真正组织起来讨论这些最新的发现。这次会议就是为了满足这一需要。通过这样做，它将促进上述复杂几何和几何分析领域的许多领域的合作。这两个领域的最新突破将呈现给新一代数学家，特别是妇女和少数群体的数学家。会议将为高级数学家提供一个论坛，通过为研究生组织一个可选的海报演示来与研究生互动，该演示将在一个非恐吓和轻松的环境中进行。还将为女性发言者提供充分的机会介绍她们的研究成果，每天至少安排一位女性发言者发言。此外，会议将为博士后和初级研究人员提供一个展示他们工作的平台。与会者将了解该领域的所有最新发展，并将在迈阿密冬季提供的诱人环境中获得新的研究途径。更具体地说，复杂几何中的特殊度量会议将集中讨论复杂几何和几何分析之间的相互作用，重点放在构造具有规定曲率属性的Hermitian度量和Kahler度量时产生的方程，例如Kahler几何中的复Monge-Ampere方程。这些方程是几何分析中出现的最重要的方程之一，了解它们的结构和求解它们所涉及的技术对于该领域的进一步发展至关重要。最近的突破包括Li，Conlon-Rochon和Szekelyidi在三维及更大维复仿射空间上独立构造了具有最大体积增长的非平坦Ricci-Flat Kahler度量，分别由Conlon-Deruelle和Biquard-Macbeth构造了梯度展开和定常Kahler-Ricci孤子的新例子，Chen-cheng解决了Tian的一个重大猜想，该猜想表明紧致Kahler流形上恒定标量曲率Kahler度量的存在与Mabuchi K-能量的充分性之间的等价性，以及最近Hein-Sun-Viaclovsky-Zhang在K3曲面上展示的Ricci-Flat Kahler度量族，K3曲面塌陷到一个区间，Tian-Yau和Taub-NUT度量族作为气泡出现。这些话题都将成为2021年1月大会讨论的一部分。更多细节将在http://faculty.fiu.edu/~rconlon/conference.htmThis上公布，该奖项反映了国家科学基金会的法定使命，并已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 Conference on Special Metrics in Complex Geometry will be held at Florida International University from January 7-10, 2021. Complex manifolds are higher-dimensional surfaces that are defined using the complex numbers. Recently, there has been significant progress in the study of "metrics" on complex manifolds, objects that endow these spaces with a shape or more precisely, curvature. The study of these metrics lies at the nexus of complex geometry and geometric analysis. The aim of this conference is to gather together experts working in these two fields to discuss these new and exciting developments. Even though lately there have been many conferences in complex geometry, none have really been organised to address these recent discoveries. This conference serves to fulfill this necessity. In doing so, it will promote collaboration across many areas of the aforementioned fields of complex geometry and geometric analysis. The latest breakthroughs in these two fields will be presented to a new generation of mathematicians, with a particular emphasis on women and those from minority groups. The conference will provide a forum for senior mathematicians to interact with graduate students through the organisation of an optional poster presentation for graduate students which will take place in a non-intimidating and relaxed environment. Ample opportunity will also be provided to women speakers to present their research, with at least one talk per day scheduled for a female speaker. Moreover, the conference will provide a platform for postdocs and junior researchers to present their work. Participants will be brought up-to-date with all of the current developments in the field and will be presented with new avenues of research in the enticing environment that Miami provides in the Winter. More specifically, the Conference on Special Metrics in Complex Geometry will concentrate on the interplay between complex geometry and geometric analysis, with an emphasis being given to equations arising in the construction of hermitian and Kahler metrics with prescribed curvature properties, for example, the complex Monge-Ampere equation in Kahler geometry. These equations are among the most important appearing in geometric analysis and understanding their structure and the techniques involved in their solution are paramount for further progress in the field. Recent breakthroughs include, among others, the independent construction of non-flat Ricci-flat Kahler metrics with maximal volume growth on complex affine space of dimensions three and greater by Li, Conlon-Rochon, and Szekelyhidi, the construction of new examples of gradient expanding and steady Kahler-Ricci solitons by Conlon-Deruelle and Biquard-Macbeth respectively, the solution by Chen-Cheng of a major conjecture of Tian stating the equivalence between the existence of constant scalar curvature Kahler metrics on a compact Kahler manifold and the properness of Mabuchi's K-energy, and the recent families of Ricci-flat Kahler metrics exhibited by Hein-Sun-Viaclovsky-Zhang on K3 surfaces which collapse to an interval with Tian-Yau and Taub-NUT metrics occurring as bubbles. These topics will all form part of the conversation at the conference in January 2021. More details will be available at http://faculty.fiu.edu/~rconlon/conference.htmThis 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.