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

本提案将促进美国参加“算术与复双曲几何界面的丢番图近似和值分布理论：小型课程研究研讨会”国际研讨会。该活动将于2019年5月13日至17日在魁北克大学蒙特利尔分校（UQAM）举行。研讨会将围绕在射影变体的分类、算术和模的基础方向上的惊人最新进展，包括丢番图近似、值分布理论和双曲几何的主题。研讨会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，并允许传播和详细研究最近的成果。讲习班的一大亮点是彼得罗·科瓦贾和阿里扬·雅万佩卡尔教授将讲授两门小型课程。研讨会的具体主题包括丢芬图近似，有理点和全纯曲线，模空间的双曲性，以及多序轴的直接像。主要目标是关注Vojta和Lang的主要猜想及其周围的进展，重点是对轨道、模空间和附近几何物体的算术和双曲几何产生影响的结果。同时讨论这些主题将促进思想的交流，并加强这些领域之间的现有互动。更多的细节可以在会议的网页上找到：http://cirget.uqam.ca/Diophantine//en/index.htmlThis该奖项反映了美国国家科学基金会的法定使命，并通过基金会的智力价值和更广泛的影响审查标准进行评估，认为值得支持。

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.