Grant: Discovery Grants Program - Individual

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. t-structures are a way to study some mathematical objects by cutting them up into smaller pieces. Different t-structures cut things in different ways. In the same what that if you take a piece of rock and cut it at different angles you will see different things, so using a different t-structure will let you see different information. I am working on understanding what the possible t-structures are. I also try to see which of the t-structures give complete information about the objects and their relationships.