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.

该奖项为美国数学家参加题为“主题月：复杂几何”的纯数学会议提供部分支持，该会议将于 2019 年 1 月 28 日至 3 月 1 日在法国卢米尼 CIRM 举行。会议的主题是几何；现代数学的基石之一，具有广泛的应用，从弦理论到密码学。 通过新发现的几何研究各个活跃领域（包括算术、代数和复微分几何）之间的深刻联系，每个学科都见证了意想不到的突破性进展。该会议旨在促进这些不同领域的研究人员之间的互动，以进一步推动这些发展。事实证明，此类活动对于这些相互关联领域的几何学家来说具有无与伦比的重要性，特别是对于那些处于职业生涯早期阶段的几何学家。该奖项支持的活动由大师班（为期 1 周）和 4 个国际会议组成，每个会议一周：凯勒几何中的奇异度量（第 2 周）、双有理几何和霍奇理论（第 3 周）、整个曲线、有理曲线和叶状结构（周） 4）和球商曲面和格子（第 5 周）。在过去的几年里，我们对复杂代数簇以及更一般的凯勒簇的几何理解取得了重要进展。这次会议的目的是促进各个活跃研究领域的国际知名专家的聚集。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：霍奇理论、K3曲面和流形上的特殊度量。第二周的目标是研究奇异度量理论发挥重要作用的各种几何问题。这包括以下主题：奇异凯勒-爱因斯坦簇及其模、复杂几何中的正性和广义丘田唐纳森猜想。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。以下主题将特别重要：霍奇理论和高维簇的模。第四周的目标是聚集不同领域的专家，研究复杂类型的代数和超越曲线的几何。主题包括：射流空间和叶理、特殊品种和内万林纳理论。尽管对球商曲面的几何构造进行了深入的研究，但通过显式方程获得的例子却很少。最近，Cartwright 和 Steger 为此类构造引入了新算法，从而完成了假射影平面的分类。最后一周的重点将是对这项基础工作及其应用的详细分析。会议网页：https://conferences.cirm-math.fr/2060.html 该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。