JAMI Conference on Higher Dimensional Algebraic Geometry

JAMI 高维代数几何会议

• 批准号: 1933539
• 负责人: David Savitt
• 金额: $ 4万
• 依托单位: Johns Hopkins University
• 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: 2019-11-01 至 2022-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1933539&HistoricalAwards=false
• 关键词: JAMI; Conference; Higher; Dimensional; Algebraic

The Johns Hopkins University Department of Mathematics, together with the Japan-U.S. Mathematics Institute, will organize a week long conference: "Recent progress in higher dimensional algebraic geometry" from March 16-22, 2020 at the Johns Hopkins University. The conference website is: https://sites.google.com/view/jami-program-2019-2020/home. It will be organized by Caucher Birkar (University of Cambridge), Christopher Hacon (the University of Utah), Chenyang Xu (M.I.T.), and Jingjun Han (Johns Hopkins University, Internal Organizer). Additional Japanese Principal Organizers are Keiji Oguiso (University of Tokyo) and Shunsuke Takagi (University of Tokyo). The main focus of the proposed activity will be on topics related to the Minimal Model Program (MMP). An algebraic variety is a shape defined by polynomial equations, and the MMP seeks to classify and understand the structure of algebraic varieties up to what is called "birational equivalence." Understanding the structure of algebraic varieties is of fundamental importance in algebraic geometry and is also of interest in other areas of mathematics (e.g., mathematical physics, computational geometry, and number theory) and in related disciplines (e.g., statistics, coding theory, complexity theory, and communications). Conference funds will support transportation and lodging costs for U.S. mathematicians that will participate in the conference, and will principally support graduate students and early-career mathematicians who do not have other sources of sponsorship.The MMP and its applications to the study of higher dimensional algebraic varieties has matured rapidly in the last 40 years and has produced many exciting results. In the last 15 years, several breakthroughs, including the finite generation of canonical rings, the existence of flips, the ACC (ascending chain condition) for log canonical thresholds, and most recently, the Borisov-Alexeev-Borisov Conjecture (the boundedness of Fano varieties with mild singularities), were inspired by seminal works of Shokurov. It is the purpose of the proposed conference to cover the latest developments concerning the structure of higher dimensional varieties.This 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.

约翰霍普金斯大学数学系与日美合作。数学研究所将于2020年3月16日至22日在约翰霍普金斯大学组织为期一周的会议：“高维代数几何的最新进展”。会议网址为：https://sites.google.com/view/jami-program-2019-2020/home。会议将由剑桥大学的Caucher Birkar、犹他大学的Christopher Hacon、麻省理工学院的徐晨阳、约翰霍普金斯大学的韩景军等人组织。其他日本主要组织者是Keiji Oguiso（东京大学）和Shunsuke Takagi（东京大学）。拟议活动的主要重点将是与最小模型计划（MMP）相关的主题。代数变量是由多项式方程定义的形状，而MMP试图对代数变量的结构进行分类和理解，直到所谓的“双域等价”。理解代数变体的结构在代数几何中是至关重要的，在其他数学领域（如数学物理、计算几何和数论）和相关学科（如统计学、编码理论、复杂性理论和通信）中也是如此。会议资金将用于支持参加会议的美国数学家的交通和住宿费用，并将主要用于支持没有其他赞助来源的研究生和早期职业数学家。近40年来，MMP及其在高维代数变异研究中的应用迅速成熟，并取得了许多令人振奋的成果。在过去的15年里，一些突破，包括正则环的有限生成，翻转的存在，对数正则阈值的ACC（上升链条件），以及最近的Borisov-Alexeev-Borisov猜想（具有轻微奇点的Fano变种的有界性），都受到了Shokurov开创性作品的启发。会议的目的是讨论有关高维品种结构的最新发展。该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。