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


Funding source

Swedish Research Council - Vetenskapsrådet (VR)


Project Details

Start date: 01/01/2017
End date: 31/12/2020
Funding: 2800000 SEK


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.


Last updated on 2017-06-10 at 08:07