Mathematical Sciences: Presidential Young Investigator Award

首席研究员将继续研究 相交上同调，而部分支持这个 总统青年调查员奖。 特别是，他会 致力于证明波莱尔猜想， 他的解决方案与L。Zucker猜想的Saper。 在两 其他项目，他将研究奇异代数簇和 几何解释的zeta函数出现在他的 指数定理 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， 同调理论的空间本身是分等级的，由他们的 代数连通性 主要研究者 将致力于解决一个关于平方的深刻猜想， 与交上同调相关的可积上同调。

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 L. Saper of the Zucker conjecture. In two other projects, he will study singular algebraic varieties and a geometric interpretation of the zeta functions arising in his index theorem. 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.