Mathematical Sciences: Hodge Structures and L2 Cohomology

小行星9505040 拟议的研究与霍奇理论的奇异或非紧品种。研究者提出将射影簇的交上同调实现为配备Hodge过滤的微分形式的显式复体。他还建议建设调和自守代表德拉姆上同调类的局部对称空间。 变种是几何和代数的中心对象，因为它们作为各种维度的多项式方程的解而出现。交上同调是一种通过观察它们的各种相交性质来理解这些变种如何在空间中定位的方法。

9505040 Stern The proposed research has to do with the Hodge theory of singular or noncompact varieties. The investigator proposes to realize the intersection cohomology of a projective variety as an explicit complex of differential forms equipped with a Hodge filtration. He also proposes to construct harmonic automorphic representatives of de Rham cohomology classes of locally symmetric spaces. Varieties are a central object in geometry and algebra as they arise as solutions to polynomial equations in various dimensions. Intersection cohomology is a way to understand how these varieties are situated in space by looking at their various intersection properties.