Topology of moduli spaces

有许多方法可以形成数学对象的空间，或者某个固定对象的子对象的空间，研究这些空间的拓扑结构通常是相当有趣的。例如光滑流形的模空间，它给微分同构群的研究提供了一个新的视角，经典的例子如位形空间及其变体，或曲率条件下的黎曼度量空间。来自同伦理论的越来越复杂的技术被用来检验这样的空间。这个项目将利用这些方法来研究这样的问题：不同的数学对象是否具有等价的模空间？

There are many ways of forming spaces of mathematical objects, or of subobjects of some fixed one, and it is usually of considerable interest to examine the topology of such spaces. Examples are moduli spaces of smooth manifolds, giving a new perspective on the study of diffeomorphism groups, classical examples such as configuration spaces and their variants, or spaces of Riemannian metrics subject to curvature conditions. Increasingly sophisticated techniques from homotopy theory are being used to examine such spaces. This project will deploy such methods to investigate questions such as: can distinct mathematical objects have equivalent moduli spaces?