Related papers: The derived moduli stack of logarithmic flat conne…

In this paper we study the moduli stack of complexes of vector bundles (with chain isomorphisms) over a smooth projective variety $X$ via derived algebraic geometry. We prove that if $X$ is a Calabi-Yau variety of dimension $d$ then this…

This is a report on recent progress concerning the interactions between derived algebraic geometry and deformation quantization. We present the notion of derived algebraic stacks, of shifted symplectic and Poisson structures, as well as the…

We establish normal form theorems for a large class of singular flat connections on complex manifolds, including connections with logarithmic poles along weighted homogeneous Saito free divisors. As a result, we show that the moduli spaces…

We study the moduli of G-local systems on smooth but not necessarily proper complex algebraic varieties. We show that, when suitably considered as derived algebraic stacks, they carry natural Poisson structures, generalizing the well known…

In this paper we study the symplectic and Poisson geometry of moduli spaces of flat connections over quilted surfaces. These are surfaces where the structure group varies from region to region in the surface, and where a reduction (or…

We study moduli spaces of flat connections on surfaces with boundary, with boundary conditions given by Lagrangian Lie subalgebras. The resulting symplectic manifolds are closely related with Poisson-Lie groups and their algebraic structure…

We consider the space of graph connections (lattice gauge fields) which can be endowed with a Poisson structure in terms of a ciliated fat graph. (A ciliated fat graph is a graph with a fixed linear order of ends of edges at each vertex.)…

The goal of this paper is to show that Stokes data coming from flat bundles form a locally geometric derived stack locally of finite presentation. This generalizes existing geometricity results on Stokes data in four different directions:…

We review recent results and ongoing investigations of the symplectic and Poisson geometry of derived moduli spaces, and describe applications to deformation quantization of such spaces.

We introduce frameworks for constructing global derived moduli stacks associated to a broad range of problems, bridging the gap between the concrete and abstract conceptions of derived moduli. Our three approaches are via differential…

We give a comparative description of the Poisson structures on the moduli spaces of flat connections on real surfaces and holomorphic Poisson structures on the moduli spaces of holomorphic bundles on complex surfaces. The symplectic leaves…

We introduce the notion of the moduli stack of relations of a quiver. When the quiver with relations is derived-equivalent to an algebraic variety, the corresponding compact moduli scheme can be viewed as a compact moduli of noncommutative…

We are interested in studying moduli spaces of rank 2 logarithmic connections on elliptic curves having two poles. To do so, we investigate certain logarithmic rank 2 connections defined on the Riemann sphere and a transformation rule to…

Let $X$ be a compact Riemann surface of genus $g \geq 3$. We consider the moduli space of holomorphic connections over $X$ and the moduli space of logarithmic connections singular over a finite subset of $X$ with fixed residues. We…

We introduce and study the derived moduli stack $\mathrm{Symp}(X,n)$ of $n$-shifted symplectic structures on a given derived stack $X$, as introduced by [PTVV] (IHES Vol. 117, 2013). In particular, under reasonable assumptions on $X$, we…

Let G be a Lie group endowed with a bi-invariant pseudo-Riemannian metric. Then the moduli space of flat connections on a principal G-bundle, P\to \Sigma, over a compact oriented surface, \Sigma, carries a Poisson structure. If we…

We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…

This paper is the sequel to [PTVV] (IHES Vol. 117, 2013). We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and polyvector fields. We then introduce the formalism of…

Let Spec(A) be an affine derived stack. We give two proofs of the existence of a canonical map from the moduli space of shifted Poisson structures (in the sense of Pantev-To\"en-Vaqui\'e-Vezzosi, see http://arxiv.org/abs/1111.3209 ) on…

We construct a proper moduli space which is a Deligne-Mumford stack parametrising quasimaps relative to a simple normal crossings divisor in any genus using logarithmic geometry. We show this moduli space admits a virtual fundamental class…