Related papers: The harmonic $2$-forms on $K3$ surfaces converging…

The author has elsewhere given a complete classification of those compact oriented Einstein 4-manifolds on which the self-dual Weyl curvature is everywhere positive in the direction of some self-dual harmonic 2-form. In this article,…

Let X be a compact 4-manifold with boundary. We study the space of hyperk\"ahler triples on X, modulo diffeomorphisms which are the identity on the boundary. We prove that this moduli space is a smooth infinite-dimensional manifold and…

We bound the $L^2$-norm of an $L^2$ harmonic $1$-form in an orientable cusped hyperbolic $3$-manifold $M$ by its topological complexity, measured by the Thurston norm, up to a constant depending on $M$. It generalizes two inequalities of…

We propose non-supersymmetric analogues of 6d N=2 Type II/heterotic dualities via a quotient of a K3 surface: an Enriques surface. We start from Type~II strings on a K3 surface and construct orbifold theories using an involution of K3. We…

We study nearly parallel $\mathrm{G}_{2}$-structures with a three-torus symmetry via multi-moment map techniques. An effective three-torus action on a nearly parallel $\mathrm{G}_{2}$-manifold yields a multi-moment map. The torus acts…

In the present work the Calderbank-Pedersen description of four dimensional manifolds with self-dual Weyl tensor is used to obtain examples of quaternionic-kahler metrics with two commuting isometries. The eigenfunctions of the hyperbolic…

The local structure of 4-dimensional, conformally flat, almost $\epsilon$-K\"ahlerian (i.e., almost pseudo-K\"ahlerian and almost para-K\"ahlerian) manifolds is characterized with the help of left-regular and right-regular paraquaternionic…

We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly non-compact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to non-compact…

We complete the classification of order $5$ nonsymplectic automorphisms on hyper-K\"ahler fourfolds deformation equivalent to the Hilbert square of a K3 surface. We then compute the topological Lefschetz number of natural automorphisms of…

We give new and rather general gluing theorems for anti-self-dual (ASD) conformal structures, following the method suggested by Floer. The main result is a gluing theorem for pairs of conformally ASD manifolds `joined' across a common piece…

Motivated by an analogous result for K3 models, we classify all groups of symmetries of non-linear sigma models on a torus T^4 that preserve the N=(4,4) superconformal algebra. The resulting symmetry groups are isomorphic to certain…

We investigate the AdS$_3$/CFT$_2$ correspondence for the Euclidean AdS$_3$ space compactified on a solid torus with the CFT field on the regularizing boundary surface in the bulk. Correlation functions corresponding to the bulk theory at…

The third real de Rham cohomology of compact homogeneous spaces is studied. Given $M=G/K$ with $G$ compact semisimple, we first show that each bi-invariant symmetric bilinear form $Q$ on $\mathfrak{g}$ such that…

Let $M$ be an $n$-dimensional $d$-bounded Stein manifold $M$, i.e., a complex $n$-dimensional manifold $M$ admitting a smooth strictly plurisubharmonic exhaustion $\rho$ and endowed with the K\"ahler metric whose fundamental form is…

Motivated by a problem of Hirzebruch, we study $8$-dimensional, closed, symplectic manifolds having a Hamiltonian torus action with isolated fixed points and second Betti number equal to $1$. Such manifolds are automatically positive…

We study the mechanisms of the non properness of the action of the group of diffeomorphisms on the space of Lorentzian metrics of a compact manifold. In particular, we prove that nonproperness entails the presence of lightlike geodesic…

In the first part we survey some of the known results and conjectures on compact Hyperkaehler (HK) manifolds. In the second part we presents a program which aims to show that HK four-folds whose second cohomology (with 4-tuple cup-product)…

In this paper, we study the expansions of Ricci flat metrics in harmonic coordinates about the infinity of ALE (asymptotically local Euclidean) manifolds.

We prove that any compact selfdual Einstein 4-orbifold of positive scalar curvature whose isometry group contains a 2-torus is, up to an orbifold covering, a quaternion Kaehler quotient of (k-1)-dimensional quaternionic projective space by…

We consider codimension 2 sphere congruences in pseudo-conformal geometry that are harmonic with respect to the conformal structure of an orthogonal surface. We characterise the orthogonal surfaces of such congruences as either $S$-Willmore…