JAMI Conference on Higher Dimensional Algebraic Geometry

约翰霍普金斯大学数学系与日美数学研究所将于2020年3月16日至22日在约翰霍普金斯大学举办为期一周的会议：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.它将由Caucher Birkar(剑桥大学)、Christopher Hacon(犹他大学)、徐晨阳(麻省理工学院)和韩京军(约翰霍普金斯大学，内部组织者)组织。其他日本的主要组织者是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方案有关的主题。代数族是由多项式等式定义的形状，而MM寻求对代数族的结构进行分类和理解，直到所谓的“二元等价性”。了解代数簇的结构在代数几何中是非常重要的，对数学的其他领域(例如，数学物理、计算几何和数论)以及相关学科(例如，统计学、编码理论、复杂性理论和通信)也很感兴趣。会议资金将为参加会议的美国数学家提供交通费和住宿费，并将主要支持没有其他赞助来源的研究生和职业生涯早期的数学家。在过去的40年里，MP及其在高维代数簇研究中的应用已经迅速成熟，并产生了许多令人兴奋的结果。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，对数正则门限的升链条件，以及最近的鲍里索夫-阿列克谢夫-鲍里索夫猜想(具有温和奇异性的Fano簇的有界性)，都受到了Shokurov的开创性工作的启发。建议召开的会议的目的是涵盖有关更高维度多样性结构的最新发展。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.