Mathematical Sciences: Presidential Young Investigator Award

首席研究员将在获得总统青年研究员奖的部分支持下继续他的交叉上同学研究。特别是，他将致力于证明Borel猜想，这将扩展他的解决方案与斯特恩先生的扎克猜想和更早的麦克弗森猜想的解决方案。在另外两个项目中，他将研究具有非孤立奇点的代数变量和直接和的交上同调上的完全Kahler度量。上同调是同调的对偶。在上同调理论中，研究了拓扑空间上的函数空间，而在同调理论中，空间本身是由它们的代数连通性来分级的。主要研究者将致力于解决一个与交点上同调有关的平方可积上同调的深层猜想。

The principal investigator will continue his studies of intersection cohomology while partially supported by this Presidential Young Investigator award. In particular, he will work towards a proof of the Borel conjecture which would extend his solution with M. Stern of the Zucker conjecture and an earlier solution to the MacPherson conjecture. In two other projects, he will study complete Kahler metrics on algebraic varieties with non-isolated singularities and intersection cohomologies which are direct summands. Cohomology is the dual of homology. In cohomology theory spaces of functions on topological spaces are studied, while in homology theory the spaces themselves are graded by their algebraic connectivity properties. The principal investigator will work toward solving a deep conjecture concerning square- integrable cohomology as related to intersection cohomology.