Related papers: Instantons on cylindrical manifolds and stable bun…

We provide a systematic way of calculating a quiver region associated to a given exceptional collection, which as an application is used to prove that $\mu$-stable sheaves represented by $2$-step complexes are Bridgeland stable. In the…

We give the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2d Yang-Mills theories that interpolate between initial and final string configurations. They satisfy the Hitchin equations with special…

Let $X$ be a closed $6-$dimensional manifold with a half-closed $SU(3)-$structure. On the product manifold $X\times S^{1}$, with respect to the product $G_{2}-$structure and on a pullback vector bundle from $X$, we show that any…

We prove the rationality and irreducibility of the moduli space of---what we call---the endomorphism-general instanton vector bundles of arbitrary rank on the projective space. In particular, we deduce the rationality of the moduli spaces…

We prove a closed formula counting semistable twisted Higgs bundles of fixed rank and degree over a smooth projective curve defined over a finite field. We also prove a formula for the Donaldson-Thomas invariants of the moduli spaces of…

We determine the instanton corrected hypermultiplet moduli space in type IIB compactifications near a Calabi-Yau conifold point where the size of a two-cycle shrinks to zero. We show that D1-instantons resolve the conifold singularity…

In the description of the instanton Floer homology of a surface times a circle due to Mu\~{n}oz, we compute the nilpotency degree of the endomorphism $u^2-64$. We then compute the framed instanton homology of a surface times a circle with…

On P3, we show that mathematical instantons in characteristic two are unobstructed. We produce upper bounds for the dimension of the moduli space of stable rank two bundles on P3 in characteristic two. In cases where there is a phenomenon…

The Hodge Conjecture is equivalent to a statement about conditions under which a complex vector bundle on a smooth complex projective variety admits a holomorphic structure. I advertise a class of abelian four-folds due to Mumford where…

In this paper we study ${\rm Spin}(7)$-instantons on asymptotically conical ${\rm Spin}(7)$-orbifolds (and manifolds) obtained by filling in certain squashed $3$-Sasakian $7$-manifolds. We construct a $1$-parameter family of explicit ${\rm…

We consider pure $SU(2)$ Yang-Mills theory when the space is compactified to a 3-dimensional sphere with finite radius. The Euclidean classical self-dual solutions of the equations of motion (the instantons) and the static finite energy…

We study the question of whether a sequence of non-instanton Yang-Mills connections can limit to a bubbling configuration composed only of instantons. In the case that the Uhlenbeck limit and the bubbles are of opposite charge, we determine…

We give a complete description of the behaviour of Calabi-Yau instantons and monopoles with an $SU(2)^2$-symmetry, on Calabi-Yau 3-folds with asymptotically conical geometry and $SU(2)^2$ acting with co-homogeneity one. We consider gauge…

We study homogeneous instantons on the seven dimensional Stiefel manifold V in the context of $G_2$ and Sasakian geometry. According to the reductive decomposition of V we provide an explicit description of all invariant $G_2$ and Sasakian…

In this paper, we prove that the tangent bundle of the moduli space $\cSU_C(r,d)$ of stable bundles of rank $r>2$ and of fixed determinant of degree $d$ (such that $(r,d)=1$), on a smooth projective curve $C$ is always stable, in the sense…

Let K be a a Lie group, modeled on a locally convex space, and M a finite-dimensional paracompact manifold with corners. We show that each continuous principal K-bundle over M is continuously equivalent to a smooth one and that two smooth…

This paper is a short version of some joint work with Stefan Haller. It describes the structure of "smooth manifold with corners" on the space of possibly broken instantons and on the completion of unstable manifolds of a generic smooth…

We prove that the moduli space of mathematical instanton bundles on ${\Bbb P}^3$ with $c_2=5$ is smooth.

We produce an equality between the Gromov-Witten invariants of the moduli space M of rank two odd degree stable vector bundles over a Riemann surface $\Sigma$ and the Donaldson invariants of the algebraic surface $\Sigma \times P^1$. We…

For an elliptic surface $q:Y \to \Sigma$, with prescribed singular fibres, Stefan Bauer proved directly via algebraic geometry that the stable bundles over $Y$, whose chern classes are pull backs from $\Sigma$, correspond to the stable…