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 …

We review and elaborate on certain aspects of the connections between instanton counting
in maximally supersymmetric gauge theories and the computation of enumerative invariants …

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 …

A ℤ 2× ℤ 2-graded generalisation of the quantum superplane is proposed and studied. We
construct a bicovariant calculus on what we shall refer to as the double-graded quantum …

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 establish a noncommutative generalisation of the Borel-Weil theorem for the
Heckenberger-Kolb calculi of the quantum Grassmannians. The result is formulated in the …

We survey some features of equivariant instanton partition functions of topological gauge
theories on four and six dimensional toric Kähler varieties, and their geometric and algebraic …

We continue our study of the noncommutative algebraic and differential geometry of a
particular class of deformations of toric varieties, focusing on aspects pertinent to the …

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 …