The derived moduli stack of logarithmic flat connections
Consider a weighted homogeneous polynomial f:Ck→C. For example, f=x2−y3:C2→C. In this talk I will discuss the moduli space of flat connections on Ck which have logarithmic singularities along D=f−1(0). This naturally has the structure of an infinite-dimensional derived moduli stack, but under a certain condition on D (namely that it is a `free divisor') there is an equivalent finite-dimensional model. In the talk I will describe this finite-dimensional model and discuss the proof of the equivalence.
I will try to make the talk expository, and will not assume any prior knowledge of derived geometry. In particular, I will introduce the notion of `bundles of curved differential graded Lie algebras' (due to Behrend and collaborators) which provides a relatively concrete and down to earth model for derived geometry.
If there is time, I will discuss the case of f=xp−yq:C2→C, which already seems to exhibit a lot of interesting behaviours.