# Calculus of functors, moduli spaces of graphs, and spaces of embeddings

Funding source

Swedish Research Council - Vetenskapsrådet (VR) |

Project Details

Description

Manifolds are high-dimensional generalizations of curves and surfaces.

They are of central importance in modern mathematics. Our goal is to

study embeddings of manifolds. For example, we consider embeddings of an

m-dimensional sphere in an n-dimensional space, for all possible m and

n. Rather than focusing on the properties of this space for a particular

value of m and n, we gain insight from studying how the space depends

on the dimensions. This is inspired by differential calculus, where

rather than just studying specific values of functions, one pays a lot

of attention the rate of change of functions. With our approach we can

connect embeddings paces with other important mathematical objects, some

of which may appear unrelated at first. Examples include moduli spaces

of graphs and algebraic K-theory. I expect that in the long term the

project will lead to interesting new invariants of manifolds and

embeddings.

The research is going to be carried at the University

of Stockholm. In addition to myself, I plan to engage at least one

graduate student and one postdoc in the project. I am involved in

several international collaborations that concern closely related

matters. There is no doubt that the project will influence and be

influenced by those collaborations.