Related papers: Quantization of deformed cluster Poisson varieties
X-ray observations of galaxy clusters reveal a large range of morphologies with various degrees of disturbance, showing that the assumptions of hydrostatic equilibrium and spherical shape which are used to determine the cluster mass from…
The understanding of clustering aspects at the ground state of nuclei and in fast rotating ones within the framework of covariant density functional theory has been reviewed and reanalyzed. The appearance of many exotic nuclear shapes in…
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…
The existence of a strict deformation quantization of $X_k=S(M_k({\mathbb{C}}))$, the state space of the $k\times k$ matrices $M_k({\mathbb{C}})$ which is canonically a compact Poisson manifold (with stratified boundary) has recently been…
We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector space $X$. The result implies in particular that the Kontsevich deformation quantizations of $\mathrm{S}(X^*)$ and $\wedge(X)$ associated with a…
In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…
We use the theory of the quantum group $U_q(gl(2,\RR))$ in order to develop a quantum theory of invariants and show a decomposition of invariants into a Gordan-Capelli series. Higher binary forms are introduced on the basis of braided…
Starting with the well-defined product of quantum fields at two spacetime points, we explore an associated Poisson structure for classical field theories within the deformation quantization formalism. We realize that the induced…
We investigate the clustering morphology of a swarm of freely rising deformable bubbles. A three-dimensional Vorono\"i analysis enables us to quantitatively distinguish between two typical clustering configurations: preferential clustering…
We give a simple formula for the operator C_3 of the standard deformation quantization with separation of variables on a K\"ahler manifold M. Unlike C_1 and C_2, this operator can not be expressed in terms of the K\"ahler-Poisson tensor on…
A factorization formula for certain automorphisms of a Poisson algebra associated to a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing…
There is a simple and natural quantization of differential forms on odd Poisson supermanifolds, given by the relation [f,dg]={f,g} for any two functions f and g. We notice that this non-commutative differential algebra has a geometrical…
We study the problem of deformation quantization for (algebraic) symplectic manifolds over a base field of positive characteristic. We prove a reasonably complete classification theorem for one class of such quantizations; in the course of…
We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then we consider a $Z[\hbar]$-algebra satisfying some suitable conditions and prove…
We classify all SL(2,R)-covariant Poisson structures on the Lobachevsky plane with respect to all multiplicative Poisson structures on SL(2,R) and describe Quantisations for all these Poisson structures.
Let $C$ be a symmetrizable generalized Cartan matrix. We introduce four different versions of double Bott-Samelson cells for every pair of positive braids in the generalized braid group associated to $C$. We prove that the decorated double…
Our aim in this thesis is to use the language of deformation-quantization to understand certain quantized algebras by looking at properties of the corresponding commutative ones, and conversely to obtain results about the commutative…
We provide a relation between the geometric framework for $q$-Painlev\'{e} equations and cluster Poisson varieties by using toric models of rational surfaces associated with $q$-Painlev\'{e} equations. We introduce the notion of seeds of…
This is an introduction to some aspects of Fomin-Zelevinsky's cluster algebras and their links with the representation theory of quivers and with Calabi-Yau triangulated categories. It is based on lectures given by the author at summer…
This paper investigates the Poisson geometry of cluster algebras and the corresponding ideal theory of quantum cluster algebras. We then show how our approach can be applied to the ring theory of quantized coordinate rings. We give a new…