A Celebration of Algebraic Geometry

21世纪的第一个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Birkar、Cascini、Hacon和McKernan对正则环有限生成的证明，以及Voisin对Kodaira猜想的反例的发现。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环、Gromov-Witten理论、变异上的有理曲线和有理点的研究以及齐次变异的上同调不变量的组合描述等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市的哈佛大学组织一场名为“代数几何的庆典”的会议，以反思这些发展，并向早期职业数学家传播这些进步。这项奖助金将支持参加会议的年轻参与者。代数几何是研究多项式方程集合的解的学科。尽管代数几何在两千多年前就开始了，随着对二次曲线（如圆）几何的研究，我们仍然不能完全回答许多简单和基本的问题。例如，给定一个多项式集合，有有限个解，我们想知道解的个数。我们在许多特殊情况下都知道这个数，这些情况在工程和生物学中有有趣的应用。21世纪的第一个十年，在这些基本问题上取得了巨大的进步。例如，Birkar, Cascini， Hacon和McKernan已经证明，给定一个多项式集合，有一个很好的方法来表示所有的解。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。这笔经费将用于支持早期职业数学家参加会议。

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.