Related papers: A Hilbert bundle description of differential K-the…

We show that M-theory on spaces with irreducible holonomy represent Type IIA backgrounds in which a collection of D6-branes wrap a supersymmetric cycle in a manifold with a holonomy group different from the one appearing in the M-theory…

For a perfect field $k$ of characteristic $p>0$ and for a finite dimensional symmetric $k$-algebra $A$ K\"ulshammer studied a sequence of ideals of the centre of $A$ using the $p$-power map on degree 0 Hochschild homology. In joint work…

We partially extend to hyperk\"ahler fourfolds of Kummer type the results that we have proved regarding stable rigid vector bundles on hyperk\"ahler (HK) varieties of type $K3^{[n]}$. Let $(M,h)$ be a general polarized HK fourfold of Kummer…

The Isomorphism Conjecture is a conceptional approach towards a calculation of the algebraic K-theory of a group ring RG, where G is an infinite group. In this paper we prove the conjecture in dimensions n<2 for fundamental groups of closed…

This expository paper details the theory of rank one Higgs bundles over a closed Riemann surface X and their relationship to representations of the fundamental group of X. We construct an equivalence between the deformation theories of flat…

We construct the Atiyah-Hirzebruch spectral sequence (AHSS) for twisted differential generalized cohomology theories. This generalizes to the twisted setting the authors' corresponding earlier construction for differential cohomology…

We define the notion of a holomorphic bundle on the noncommutative toric orbifold $T_{\theta}/G$ associated with an action of a finite cyclic group $G$ on an irrational rotation algebra. We prove that the category of such holomorphic…

Suppose $k$ is an algebraically closed field of characteristic two, let $A_4$ be an alternating group on four letters, and let $H$ be the unique Sylow two-subgroup of $A_4$. Let $X$ be a smooth projective irreducible curve over $k$ with a…

Let $G$ be an even dimensional, connected, abelian Lie group and $(\mathcal{A}^\infty,G,\alpha,\tau)$ be a $C^*$-dynamical system equipped with a faithful $G$-invariant trace $\tau$. We show that whenever it determines a…

This thesis is dedicated to the study of K-theoretical properties of D-branes and Ramond-Ramond fields. We construct abelian groups which define a homology theory on the category of CW-complexes, and prove that this homology theory is…

We study the geometry of exceptional loci of birational contractions of hyper-K\"ahler fourfolds that are of K3$^{[2]}$-type. These loci are conic bundles over K3 surfaces and we determine their classes in the Brauer group. For this we use…

We introduce a general framework to unify several variants of twisted topological $K$-theory. We focus on the role of finite dimensional real simple algebras with a product-preserving involution, showing that Grothendieck-Witt groups…

The aim of these notes is to acquaint the reader with important objects in complex algebraic geometry: K3 surfaces and their higher-dimensional analogs, hyperk\"ahler manifolds. These manifolds are interesting from several points of view:…

Recently it has been shown that D-branes in orientifolds are not always described by equivariant Real K-theory. In this paper we define a previously unstudied twisted version of equivariant Real K-theory which gives the D-brane spectrum for…

Given a complex Hilbert space H, we study the differential geometry of the manifold M of all projections in V:=L(H). Using the algebraic structure of V, a torsionfree affine connection $\nabla$ (that is invariant under the group of…

We study the dynamics of M-theory on isolated non-toric Calabi-Yau threefold singularities of type $(A_j,A_l)$ and $(A_k,D_n)$, engineering five-dimensional rank-zero SCFTs. Our approach consists in mapping these backgrounds to type IIA…

A hyperkaehler manifold with a circle action fixing just one complex structure admits a natural a hyperholomorphic line bundle. This forms the basis for the construction of a corresponding quaternionic Kaehler manifold in the work of…

K-theoretic Gromov-Witten invariants of a compact Kahler manifold $X$ are defined as super-dimensions of sheaf cohomology of interesting bundles over moduli spaces of n-pointed holomorphic curves in X. With this article, we begin a series…

We give a one-dimensional interpretation of the four-dimensional twisted N=1 superYang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does…

Let $ 1 \rightarrow N \rightarrow G \rightarrow Q \rightarrow 1$ be an exact sequence of finitely presented groups where Q is infinite and not virtually cyclic, and is the fundamental group of some closed 3-manifold. If G is Kaehler, we…