Diophantine Approximation and Value Distribution Theory at the interface of Arithmetic and Complex Hyperbolic Geometry: A Research Workshop with Minicourse

这项建议将促进美国参加国际研讨会“丢番图近似和值分布理论在算术和复杂的双曲几何的接口：一个研究讲习班与微型课程”。 该活动将于2019年5月13日至17日在蒙特利尔的魁北克大学（UQAM）举行。 该研讨会将围绕壮观的最新进展的方向是基本的分类，算术和模数的投影品种，包括丢番图近似，值分布理论和双曲几何的主题。该讲习班将汇集各级研究人员，讨论和交流不同但相互关联的领域的想法，并传播和详细研究最近的成果。讲习班的一个亮点是由Pietro Corvaja教授和Ariyan Javanpeykar教授主讲的两门微型课程。 研讨会感兴趣的具体主题包括丢番图近似，有理点和全纯曲线，模空间的双曲性，以及pluricanonical层的直接图像。一个主要的目标是集中在进展和周围的主要progratures的Vojta和郎，重点是结果有后果的算术和双曲几何的orbifolds，模空间和附近的几何对象。 同时讨论这些主题将促进各种想法的交流，并加强这些领域之间的现有互动。更多细节可以在会议网页上找到：http://cirget.uqam.ca/Diophantine//en/index.htmlThis奖项反映了NSF的法定使命，并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来支持。

This proposal will facilitate US participation in the international workshop "Diophantine Approximation and Value Distribution Theory at the interface of Arithmetic and Complex Hyperbolic Geometry: a research workshop with minicourse". The event will be held at the University of Quebec at Montreal (UQAM), Montreal, QC, during the time period 13-17 May 2019. The workshop will center around spectacular recent progress in directions that are fundamental to the classification, arithmetic, and moduli of projective varieties, including topics in Diophantine approximation, value distribution theory, and hyperbolic geometry. The workshop will bring together researchers of all levels to discuss and exchange ideas across diverse, but interrelated, fields, and allow for recent results to be disseminated and studied in detail. A highlight of the workshop is the presentation of two minicourses to be given by Professors Pietro Corvaja and Ariyan Javanpeykar. Specific topics of interest for the workshop include Diophantine approximation, rational points and holomorphic curves, hyperbolicity of moduli spaces, and direct images of pluricanonical sheaves. A primary goal is to focus on advances in and around the main conjectures of Vojta and Lang, with emphasis on results that have consequences for the arithmetic and hyperbolic geometry of orbifolds, moduli spaces and nearby geometric objects. Discussing these topics in tandem will facilitate cross-pollination of ideas and strengthen existing interactions between these areas. More details can be found on the conference webpage:http://cirget.uqam.ca/Diophantine//en/index.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.