Conference: Higher dimensional algebraic geometry

该奖项支持参加将于2024年1月10日至14日在加州大学圣地亚哥分校举行的“高维代数几何”会议。会议由帝国理工学院的Paolo Cascini、波士顿学院的Brian Lehman、加州大学圣地亚哥分校的Dragos Oprea和普林斯顿大学的徐晨阳组织。这次活动将有大约25位顶尖数学家的演讲。初出茅庐的数学家也将有机会传播他们的工作。会议将集中展示二次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取得了长足的进步。然而，由于大流行，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，促进数学界之间的联系。这项奖励将为没有联邦资助的数学家、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提供部分支持。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。在二元几何中，重点是对复杂射影簇进行分类，直到二元等价。最小模型程序的目的是将第二维的分类结果推广到更高维的种类。詹姆斯·麦科南和他的合作者的工作使这个领域发生了深刻的变化。会议的主题将包括该领域一些最令人兴奋的最新进展，如K-稳定性和Fano变元，叶和Kahler变元的最小二乘估计，Calabi-Yau变元的有界性结果，正特征和混合特征的双曲几何，镜像对称性等。会议的网站是https://lehmannb3.wixsite.com/james-60.This奖，它反映了国家科学基金会的法定使命，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。

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.