Mathematical Sciences: Algebraic Geometry

约瑟夫·哈里斯从事代数几何工作。更具体地说，他将致力于研究与曲线、K3曲面、极化簇和点的n元组的模空间有关的问题，包括它们的上同调和线丛。此外，他还将讨论有关一般曲面和三重曲面上的线性级数和曲线的极限问题。最后，他将讨论关于各种一般类型的合理点的问题。代数几何是研究由多项式方程组的零点集产生的几何对象的学科。这是最古老也是目前最活跃的数学分支之一，广泛应用于数学、物理、计算机科学等领域。哈里斯是这门学科最好的实践者之一，他不断地做出非常深刻的贡献。这一提议无疑将带来更多令人振奋的结果。

Joseph Harris works in algebraic geometry. More specifically he will work on problems connected with moduli spaces of curves, K3 surfaces, polarized varieties and n-tuples of points including their cohomology and line bundles. In addition he will address problems concerning limits of linear series and curves on general surfaces and three-folds. Finally he will look at problems concerning rational points on varieties of general type. Algebraic geometry is the study of the geometric objects arising from the sets of zeros of systems of polynomial equations. This is one of the oldest and currently one of the most active branches of mathematics with widespread applications through out mathematics and reaching into physics, computer science etc. Harris is one of the very best practitioners of this subject with his constant flow of very deep contributions. This proposal will undoubtedly lead to many more exciting results.