Mathematical Sciences: Cyclic Homology and D-Modules

这个研究项目涉及几何方面， 几种上同调理论的应用（循环同调， 等变上同调理论，椭圆上同调），以及 D模块 重要代数的循环同调 （微分和伪微分算子，群代数） 对于李群，交叉积代数）将进一步研究 并与几何学、拓扑学和表示学中的问题有关 理论 这包括与等变上同调的关系， 这将适用于李群在流形上的作用。 的 研究人员将研究几何和数论 椭圆上同调 他还将追求几个 与Hodge理论有关的D-模难题， 曲线的模空间

This research project concerns the geometrical aspects and applications of several cohomology theories (cyclic homology, equivariant cohomology theories, elliptic cohomology), and also D-modules. The cyclic homology of important algebras (differential and pseudo-differential operators, group algebras for Lie groups, crossed-product algebras) will be further studied and related to problems in geometry, topology, and representation theory. This includes relations with equivariant cohomology, which will be applied to actions of Lie groups on manifolds. The investigator will study the geometric and number-theoretic aspects of elliptic cohomology. He will also pursue several difficult questions on D-modules in relation to Hodge theory and moduli spaces of curves.