Foliation Theory in Algebraic Geometry

这笔赠款将资助早期职业数学家参加2013年9月3日至7日在纽约市西蒙斯基金会杰拉尔德·D·菲施巴赫礼堂举行的代数几何中叶理论会议。将有关于二次曲面几何、叶面、双曲线和相关学科的最新进展的讲座。这次会议将使专家们有机会向在这些领域工作的年轻人传播许多最新的进展。代数几何是研究一组多项式方程的解的学科。这始于两千多年前，研究圆锥曲线的几何学，如圆。然而，我们仍然不能完全回答许多简单和根本的问题，如寻找解决方案的数量。我们在许多特殊情况下都知道这个数字，这些情况在工程学和生物学中有有趣的应用。叶理理论研究的是微分方程组的解或流线。作为描述物理现象的微分方程，层理理论在物理和工程上都有很大的应用价值。当微分方程式的集合具有多项式系数时，代数几何和分层理论之间存在着丰富的相互作用。

This grant will fund the participation of early career mathematicians at a conference on Foliation theory in algebraic geometry to be held at the Simons Foundation's Gerald D. Fischbach Auditorium in New York City, September 3rd-7th, 2013. There will be lectures on recent advances in birational geometry, foliations, hyperbolicity and related subjects. This conference will give experts a chance to disseminate the many recent advances to young people working in these areas.Algebraic geometry is the study of the solutions to a collection of polynomial equations. This began more than two thousand years ago, with the study of the geometry of conic sections, such as circles. However we still cannot completely answer many simple and fundamental questions, such as find the number of solutions. We know this number in many special cases, and these cases have interesting applications in engineering and biology. Foliation theory studies the solutions, or flow lines, to collections of differential equations. As differential equations model physical phenomena, foliation theory is useful in physics and engineering. When the collection of differential equations have polynomial coefficients, there is a rich interplay between algebraic geometry and foliation theory.