Conference: Higher dimensional algebraic geometry

该奖项支持参加会议“高维代数几何”，将于2024年1月10日至14日在加州圣地亚哥大学举行。会议由Paolo Cascini（帝国理工学院），Brian Lehman（波士顿学院），Dragos Oprea（加州圣地亚哥大学，当地组织者）和Chenyang Xu（普林斯顿大学）组织。该活动将由大约25位领先的数学家进行演讲。也将有机会为早期职业数学家传播他们的工作。会议将聚焦双有理几何和高维代数几何的最新突破。在过去的几年里，高维代数几何的各个分支学科都取得了重大进展。然而，由于这一流行病，传播这些进展的机会有限。本次会议旨在纠正这种情况。它还旨在促进合作，促进数学界内部的联系。该奖项将提供部分支持谁没有联邦支持或谁是学生，博士后研究人员，或属于代表性不足的群体的数学家的旅费。代数簇是由多项式方程定义的几何对象。理解代数簇的结构是代数几何中的一个中心问题，在附近的领域（交换代数，微分几何，辛几何，数学物理，计算几何，数论等）具有深远的影响。在双有理几何中，重点是对复射影簇进行分类直到双有理等价。最小模型程序旨在将二维的分类结果推广到更高维的品种。詹姆斯·麦克南和他的合作者的工作深刻地改变了这个领域。会议的主题将包括该领域的一些最令人兴奋的最新进展，如K-稳定性和Fano品种，叶理和Kahler品种的MMP，Calabi-Yau品种的有界性结果，正和混合特征的双有理几何，镜像对称等。会议的网站是https://lehmannb3.wixsite.com/james-60.This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 award supports participation in the conference "Higher dimensional algebraic geometry" which will take place at the University of California San Diego from January 10 - 14, 2024. The conference is organized by Paolo Cascini (Imperial College), Brian Lehman (Boston College), Dragos Oprea (University of California San Diego, local organizer) and Chenyang Xu (Princeton University). The event will feature talks by approximately 25 leading mathematicians. There will also be opportunities for early-career mathematicians to disseminate their work. The conference will spotlight the latest breakthroughs in birational geometry and higher dimensional algebraic geometry. The past few years have witnessed significant progress in various subdisciplines of higher-dimensional algebraic geometry. However, due to the pandemic, there have been limited opportunities to disseminate these advances. The current conference seeks to remedy this situation. It also aims to foster collaborations and to facilitate connections within the mathematical community. This award will provide partial support to the travel expenses of mathematicians who do not have federal support or who are students, postdoctoral researchers, or belong to under-represented groups. Algebraic varieties are geometric objects defined by polynomial equations. Understanding the structure of algebraic varieties is a central question in algebraic geometry with far-reaching implications in nearby fields (commutative algebra, differential geometry, symplectic geometry, mathematical physics, computational geometry, number theory, etc). In birational geometry, the focus is on classifying complex projective varieties up to birational equivalence. The Minimal Model Program aims to generalize the classification results in dimension two to higher-dimensional varieties. The field was profoundly transformed by the work of James McKernan and his collaborators. The topics of the conference will include some of the most exciting recent advances in the area, such as K-stability and Fano varieties, MMP for foliations and Kahler varieties, boundedness results for Calabi-Yau varieties, birational geometry in positive and mixed characteristic, mirror symmetry and others. The website for the conference is https://lehmannb3.wixsite.com/james-60.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.