Homotopy theory and derived categories

我将研究两个主题：配置空间和t-结构。流形M可以被认为是一个物体的可能位置的空间，或者是一个机械系统的可能状态。例如M=R3，欧几里得三维空间就是我们生活的三维空间。K个点F(M，k)上的位形空间由流形上不允许碰撞的k个粒子组成。所以它们是点的序列，没有两个点是相同的。例如，它可以是具有多个手臂的机器人的状态。同样，如果我们考虑欧几里得的三个空间，那么F(R3，k)可以被认为是一个有k个行星的宇宙的可能状态。我对M和F(M，k)之间的关系特别感兴趣，我正在研究一种数学方法，从关于M的信息中获得关于F(M，k)的信息。

I will work on two topics: configuration spaces and t-structures. A manifold M can be thought of as a space of possible locations of an object or as the possible states of a mechanical system. For example M=R3, Euclidean three space is the three dimensional space we live in. The configuration space on k points F(M,k) consists of k particles in the manifold that are not allowed to collide. So they are sequences of points no two of which can be the same. For example it could be the states of a robot with many arms. Again if we think of Euclidean three space, then F(R3,k) could be thought of as the possible states of a universe with k planets in it. I am particularly interested in the relation between M and F(M,k), am working on a mathematical way of getting information about F(M,k) from information about M.