Thematic Month at CIRM in Complex Geometry

该奖项为美国参与提供部分支持-基于数学家在纯数学会议题为“专题月：复杂几何”，将于CIRM，Luminy（法国）从1月28日至3月01日，2019年。会议的主题是几何;现代数学的基石之一，具有广泛的应用，从弦论到密码学。 通过新发现的，几何研究的各个活跃领域之间的深刻联系，包括算术，代数和复微分几何，每个主题都见证了意想不到的和突破性的进展。会议旨在促进这些不同领域的研究人员之间的互动，以促进这些发展。这些活动已被证明是无与伦比的重要性，几何学家在这些相互关联的领域，特别是对那些在其职业生涯的早期阶段。（1周）和4个国际会议，每个为期一周：奇摄动在Kaehler几何（第2周），双有理几何和霍奇理论（第3周），整个曲线，有理曲线和树叶（第4周），球商曲面和晶格（第5周）。在过去的几年中，我们已经见证了重要的进展，我们的理解几何复杂的代数品种，更普遍的凯勒品种。本次会议的目的是促进在各个活跃的研究领域的国际地位的专家聚集。大师班的目的是介绍将在整个会议中使用的技术和理论。主要包括三门课程：Hodge理论，K3曲面和流形上的特殊度量。在第二周，目标是研究各种几何问题，其中奇异度量理论发挥了重要作用。其中包括以下主题：奇异凯勒-爱因斯坦簇及其模、复几何中的正性和广义姚田-唐纳森猜想。第三周的目的是研究代数几何中的各种方法，以期在双有理几何和模空间中应用。以下主题将是特别重要的：霍奇理论和模的高维品种。第四周的目标是收集专家在不同领域的工作几何代数和超越曲线的复杂品种。主题包括：喷射空间和叶理，特殊品种和Nevanlinna理论。尽管密集的搜索找到球商曲面的几何结构，很少有例子已经获得显式方程。最近Cartwright和Steger推出了新的算法，这种建设，导致完成分类的假投影平面。最后一周的重点将是对这一基础工作及其应用的详细分析。会议网页：https://conferences.cirm-math.fr/2060.htmlThis奖反映了NSF的法定使命，并已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的支持。

The award provides partial support for the participation of U.S.-based Mathematicians in a conference in Pure Mathematics titled "Thematic Month: Complex Geometry", to be held at CIRM, Luminy (France) from January 28 to March 01, 2019. The main theme of the conference is Geometry; one of the cornerstones of modern Mathematics with broad applications, ranging from String Theory to Cryptography. Through newly discovered, deep connections between various active areas of research in Geometry, including Arithmetic, Algebraic and Complex Differential Geometry, each subject has witnessed unexpected and groundbreaking advances. The conference aims to facilitate interactions among researchers in these diverse fields to further these developments. Such activities have proved to be of unparalleled importance for geometers in these interconnected areas, specially for those in early stages of their careers.The event supported by this award is composed of a master class (1 week long) and 4 international conferences, each one week long: Singular Metrics in Kaehler Geometry (week 2), Birational Geometry and Hodge Theory (week 3), Entire Curves, Rational Curves and Foliations (week 4), and Ball Quotient Surfaces and Lattices (week 5). The last couple of years have been witness to important progress in our understanding of the geometry of complex algebraic varieties, and more generally Kaehler varieties. The aim of this conference is to facilitate the gathering of experts of international stature in various active areas of research. The aim of the Master Class is the introduction of techniques and theories that will be used throughout the conference. This will mainly consist of three courses: Hodge theory, K3 surfaces and special metrics on manifolds. During the second week, the goal is to study various geometric problems where the theory of singular metrics play an important role. This includes the following topics: Singular Kaehler-Einstein varieties and their moduli, Positivity in Complex Geometry and Generalized Yau-Tian-Donaldson Conjecture. The aim of the third week is to investigate various methods in Algebraic Geometry with a view towards applications in Birational Geometry and Moduli spaces. The following topics will be of particular importance: Hodge theory and Moduli of higher dimensional varieties. The goal of the fourth week is to gather specialists in different fields working on the geometry of algebraic and transcendental curves in complex varieties. Topics include: jet spaces and foliations, Special Varieties and Nevanlinna theory. Despite an intensive search for finding a geometric construction for ball quotient surfaces, very few examples have been obtained with explicit equations. Recently Cartwright and Steger have introduced new algorithms for such constructions, leading to the completion of the classification of fake projective planes. The focus of the final week will be a detailed analysis of this fundamental work and its applications. Webpage for the conference: https://conferences.cirm-math.fr/2060.htmlThis 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.