JAMI Conference on Higher Dimensional Algebraic Geometry

Johns Hopkins University, Baltimore MD

Investigators

Abstract

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.