Thematic Month at CIRM in Complex Geometry

CIRM 复杂几何主题月

• 批准号: 1901659
• 负责人: Gabor Szekelyhidi
• 金额: $ 1.79万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-03-01 至 2020-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1901659&HistoricalAwards=false
• 关键词: Thematic; Month; CIRM; Complex; Geometry

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.

该奖项为总部位于美国的数学家参加纯数学会议的参与提供了部分支持，标题为“主题月份：复杂的几何”，将于2019年1月28日至2019年3月1日在法国的Cirm（法国）举行。会议的主要主题是几何学；现代数学的基石之一，具有广泛的应用，从弦理论到密码学不等。 通过新发现的几何研究领域的各种活跃领域（包括算术，代数和复杂的差异几何形状）之间的深厚连接，每个受试者都见证了意想不到的突破性进步。该会议旨在促进这些不同领域的研究人员之间的互动，以进一步发展这些发展。 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）以及球大体表面和格（第5周）。在过去的几年中，我们对我们对复杂代数品种的几何形状以及更普遍的Kaehler品种的几何形状进行了重要进展。这次会议的目的是促进在各个活跃研究领域的国际地位专家聚集。大师班的目的是引入整个会议中将使用的技术和理论。这将主要由三个课程组成：霍奇理论，K3表面和有关流形的特殊指标。在第二周，目标是研究各种几何问题，在这些几何问题中，奇异指标理论起着重要作用。这包括以下主题：奇异的Kaehler-Einstein品种及其模量，复杂几何形状的积极性和广义的Yau-Tian-Donaldson猜想。第三周的目的是研究代数几何形状中的各种方法，以探讨在Birational几何和模量空间中的应用。以下主题将特别重要：较高维度品种的霍奇理论和模量。第四周的目的是在复杂品种中的代数和先验曲线的几何形状的不同领域中收集专家。主题包括：喷气空间和叶子，特殊品种和内凡林纳理论。尽管对找到球表面的几何结构进行了密集的搜索，但很少有具有显式方程式的示例。最近，卡特赖特（Cartwright）和斯蒂格（Steger）引入了此类构造的新算法，从而完成了假射击飞机的分类。最后一周的重点将是对这项基本工作及其应用的详细分析。会议网页：https：//conferences.cirm-math.fr/2060.htmlthis Award反映了NSF的法定任务，并且使用基金会的知识分子优点和更广泛的影响审查标准，被认为值得通过评估来获得支持。