A Celebration of Algebraic Geometry

代数几何的庆典

• 批准号: 1045217
• 负责人: James McKernan
• 金额: $ 4.95万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-05-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1045217&HistoricalAwards=false
• 关键词: Celebration; Algebraic; Geometry

The first decade of the twenty-first century has witnessed the solution of many fundamental and long-standing problems in algebraic geometry, including the proof of finite generation of the canonical ring by Birkar, Cascini, Hacon and McKernan and the discovery of a counterexample to Kodaira's conjecture by Voisin. Furthermore, the modern techniques developed earlier in the decade have led to far-reaching advances in the cohomology and the tautological rings of the moduli space of curves, Gromov-Witten theory, the study of rational curves and rational points on varieties and combinatorial descriptions of cohomological invariants of homogeneous varieties. The PIs are organizing a conference entitled "A celebration of algebraic geometry", on August 25-28, 2011 at Harvard University in Cambridge, Massachusetts, in order to reflect on these developments and to disseminate the advances to early career mathematicians. This grant will support young participants attending the conference.Algebraic geometry is the study of the solutions to a collection of polynomial equations. Even though algebraic geometry started more than two thousand years ago, with the study of the geometry of conic sections, such as circles, we still cannot completely answer many simple and fundamental questions. For example, given a collection of polynomials, with finitely many solutions, we would like to know the number of solutions. We know this number in many special cases, and these cases have interesting applications in engineering and biology. The first decade of the twenty-first century has seen tremendousadvances on some of these fundamental problems. For example, Birkar, Cascini, Hacon and McKernan have shown that given a collection of polynomials, there is a nice way to present all of the solutions. This presentation allows us to answer many interesting questions. The PIs are organizing a conference to disseminate the advances of the last ten years to young mathematicians. This grant will support the participation of early career mathematicians at the conference.

二十一世纪的头十年见证了代数几何中许多基本和长期存在的问题的解决，包括比尔卡尔、卡西尼、哈康和麦克南证明了正则环的有限生成，以及沃辛发现了小平猜想的反例。 此外，近十年来发展起来的现代技术在曲线模空间的上同调和同义反复环、格罗莫夫-维滕理论、簇上有理曲线和有理点的研究以及同质簇的上同调不变量的组合描述方面取得了深远的进展。 PI 将于 2011 年 8 月 25 日至 28 日在马萨诸塞州剑桥的哈佛大学组织一次题为“代数几何庆典”的会议，以反思这些发展并向早期职业数学家传播这些进展。 这笔赠款将支持参加会议的年轻参与者。代数几何是对多项式方程组解的研究。 尽管代数几何在两千多年前就已开始，但随着对圆锥曲线（例如圆）几何的研究，我们仍然无法完全回答许多简单而基本的问题。 例如，给定一个具有有限多个解的多项式集合，我们想知道解的数量。 我们在许多特殊情况下都知道这个数字，这些情况在工程和生物学中有有趣的应用。二十一世纪的头十年在其中一些基本问题上取得了巨大进展。 例如，Birkar、Cascini、Hacon 和 McKernan 已经证明，给定一组多项式，有一种很好的方法来呈现所有解决方案。这个演示使我们能够回答许多有趣的问题。 PI 正在组织一次会议，向年轻数学家传播过去十年的进展。 这笔赠款将支持早期职业数学家参加会议。