Mathematical Sciences: Free Loop Space, Automorphisms of Manifolds and Cyclic Homology

Burghelea教授将研究 简单几何对象的自然变换， 紧光滑流形 这些都出现在现代物理 理论，以及在许多纯粹的数学背景下。 其他 相关事务在他的项目中也将发挥较小的作用。 具体来说，Burghelea将研究（1）的同伦类型 （resp.）紧光滑 （分别）辛）流形M和同调的关系 上用主丛定义的一些相伴空间 M. (2)自由回路的微分几何和拓扑 紧黎曼流形空间 (3)的决定因素 椭圆算子 (4)完备的有界协调 度量流形 (5)循环中的几何和代数问题 同源性

Professor Burghelea will study the topological character of natural transformations of simple geometric objects known as compact smooth manifolds. These arise in modern physical theories as well as in many purely mathematical contexts. Other related matters will also play a lesser role in his project. Specifically, Burghelea will study (1) the homotopy type of diffeomorphisms (resp. symplectomorphisms) of a compact smooth (resp. symplectic) manifold M and the relation to the homology of some associated spaces defined in terms of principal bundles over M. (2) the differential geometry and topology of the free loop space of compact Riemannian manifolds. (3) the determinants of elliptic operators. (4) the bounded concordances of complete metric manifolds. (5) geometric and algebraic problems in cyclic homology.