This is a mini-review about generalized instantons of noncommutative gauge theories in
dimensions 4, 6 and 8, with emphasis on their realizations in type II string theory, their …

The main idea behind noncommutative geometry (see [Connes (1994)] for an extensive
treatment of the subject) lies in the correspondence between spaces and algebras of …

We survey some of the AGT relations between N= 2 gauge theories in four dimensions and
geometric representations of symmetry algebras of two-dimensional conformal field theory …

We construct and study noncommutative deformations of toric varieties by combining
techniques from toric geometry, isospectral deformations, and noncommutative geometry in …

For an affine toric variety Spec (A), we give a convex geometric description of the Hodge
decomposition of its Hochschild cohomology. Under certain assumptions we compute the …

We introduce some algebraic geometric models in cosmology related to the''boundaries''of
space-time: Big Bang, Mixmaster Universe, Penrose's crossovers between aeons. We …

In this paper, we construct the ADHM quiver representations and the corresponding sheaves
as the mirror objects of formal deformations of the framed immersed Lagrangian sphere …

We describe a general procedure, based on Gerstenhaber–Schack complexes, for
extending to quantized twistor spaces the Donaldson–Friedman gluing of twistor spaces via …

We construct explicit deformation quantizations of the noncompact complex surfaces Zk WD
Tot. OP1. k//and describe their effect on moduli spaces of vector bundles and instanton …

We elaborate on the quantization of toric varieties by combining techniques from toric
geometry, isospectral deformations and noncommutative geometry in braided monoidal …