Foliation Theory in Algebraic Geometry

该基金将资助早期职业数学家参加于2013年9月3日至7日在纽约市Simons基金会的Gerald D. Fischbach礼堂举行的代数几何叶化理论会议。将会有关于几何、叶、双曲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进展。代数几何是研究多项式方程集合的解的学科。这始于两千多年前，人们开始研究圆锥曲线的几何形状，比如圆。然而，我们仍然不能完全回答许多简单而基本的问题，例如找到解决方案的数量。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。叶理理论研究微分方程组的解或流线。作为一种用微分方程模拟物理现象的理论，叶理理论在物理和工程上都有广泛的应用。当微分方程的集合具有多项式系数时，代数几何与叶理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.