Related papers: Quantization of derived cotangent stacks and gauge…

In this review we discuss several topological and geometric invariants obtained by quantizing $\sigma$-models. More precisely, we don't quantize the entire mapping stack of fields, but rather only the substack of low energy fields. The…

In this paper, we study invariant Poisson structures on homogeneous manifolds, which serve as a natural generalization of homogeneous symplectic manifolds previously explored in the literature. Our work begins by providing an algebraic…

We prove the AKSZ theorem for shifted Poisson structures: if $X$ is an $n$-shifted Poisson derived stack, and $Y$ a $d$-oriented derived stack, then the mapping stack \[\underline{\mathrm{Map}}(Y,X)\] is naturally endowed with an…

We give an explicit finite-dimensional model for the derived moduli stack of flat connections on $\mathbb{C}^k$ with logarithmic singularities along a weighted homogeneous Saito free divisor. We investigate in detail the case of plane…

The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a…

We classify in this paper Poisson structures on modules over semisimple Lie algebras arising from classical r-matrices. We then study their quantizations and the relation to classical invariant theory.

We prove that when Kontsevich's deformation quantization is applied on weight homogeneous Poisson structures, the operators in the $\ast-$ product formula are weight homogeneous. We then consider the linear Poisson case…

If G is a reductive group which acts on a linearized smooth scheme $X$ then we show that under suitable standard conditions the derived category of coherent sheaves of the corresponding GIT quotient stack $X^{ss}/G$ has a semi-orthogonal…

We define a derived enhancement of the hyperquot scheme (also known as nested Quot scheme), which classically parametrises flags of quotients of a perfect coherent sheaf on a projective scheme. We prove it is representable by a derived…

Motivated by the problem of transverse deformation quantization of foliated manifolds, we describe a quantization of Dirac structures (more precisely, of those that are formal deformations of regular ones) to stacks of algebroids in the…

Given a curved differential graded algebra $A$, we define a new model structure on the category of curved differential graded $A$-modules, called the injective Guan-Lazarev model structure. We prove that the category of CDG $A$-modules with…

Given a smooth morphism of schemes $X\rightarrow T$, denote by $\mathcal D_{X/T}^{\mathsf{cr}}$ the sheaf of rings of fiberwise crystalline differential operators on $X$ relative to $T$ and by $\Omega^\bullet_{X/T}$ the de Rham sheaf of…

We develop a version of Hodge theory for a large class of smooth formally proper quotient stacks $X/G$ analogous to Hodge theory for smooth projective schemes. We show that the noncommutative Hodge-de Rham sequence for the category of…

Drinfeld Zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of the affine Lie algebra $\hat{sl}_n$. We introduce an affine, reduced, irreducible, normal quiver variety $Z$ which…

Drinfeld zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of an affine Lie algebra $\hat g$. In case $g$ is the symplectic Lie algebra $sp_N$, we introduce an affine, reduced,…

Let A denote the ring of differential operators on the affine line with its two usual generators t and d/dt given degrees +1 and -1 respectively. Let X be the stack having coarse moduli space the affine line Spec k[z] and isotropy groups…

For any Lie groupoid $G$, the vector bundle $g^*$ dual to the associated Lie algebroid $g$ is canonically a Poisson manifold. The (reduced) C*-algebra of $G$ (as defined by A. Connes) is shown to be a strict quantization (in the sense of M.…

We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analysing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge…

As a generalization of the linear Poisson bracket on the dual space of a Lie algebra, we introduce certain non-linear Poisson brackets which are ``cocycle perturbations'' of the linear Poisson bracket. We show that these special Poisson…

In this paper, we present a theory of Poisson deformation of Hamiltonian quasi-Poisson manifolds to Hamiltonian Poisson manifolds that include degenerate cases. More significantly, this theory extends to singular cases arising from…