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We find locally free resolutions of length one for all semi-stable sheaves supported on curves of multiplicity five in the complex projective plane. In some cases we also find geometric descriptions of these sheaves by means of extensions.…

In this paper, we characterize the (left) multiplier algebra of a semidirect product algebra ${\mathcal A}={\mathcal B}\oplus {\mathcal I}$, where ${\mathcal I}$ and ${\mathcal B}$ are closed two-sided ideal and closed subalgebra of…

We construct quasi-projective moduli spaces of $K$-general lattice polarized irreducible holomorphic symplectic manifolds. Moreover, we study their Baily--Borel compactification and investigate a relation between one-dimensional boundary…

The symmetric product of vector fields on a manifold arises when one studies the controllability of certain classes of mechanical control systems. A geometric description of the symmetric product is provided using parallel transport, along…

Motivated by the supersymmetric version of Dirac's theory, chiral models in field theory, and the quest of a geometric fundament for the Standard Model, we describe an approach to the differential geometry of vector bundles on…

Morse Theory on Banach spaces would be a useful tool in nonlinear analysis but its development is hindered by many technical problems. In this paper we present an approach based on a new notion of generalized functions called…

We extend Donaldson's asymptotically holomorphic techniques to symplectic orbifolds. More precisely, given a symplectic orbifold such that the symplectic form defines an integer cohomology class, we prove that there exist sections of large…

We consider the class of quantum mechanical master equations defined on a generic Banach space, arising by projecting weakly perturbed one-parameter groups of isometries. We show that the possible semigroup approximations are far from…

We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. Many of the presented…

We obtain a exponential large deviation upper bound for continuous observables on suspension semiflows over a non-uniformly expanding base transformation with non-flat singularities or criticalities, where the roof function defining the…

We study several categories of analytic stacks relative to the category of bornological modules over a Banach ring. When the underlying Banach ring is a non-Archimedean valued field, this category contains derived rigid analytic spaces as a…

Studying degenerations of moduli spaces of semistable principal bundles on smooth curves leads to the problem of constructing and studying moduli spaces on singular curves. In this note, we will see that the moduli spaces of…

We construct a universal partial compactification of the relative moduli space of semistable meromorphic Higgs bundles over the stack of stable pointed curves. It parametrizes meromorphic Gieseker Higgs bundles, and is equipped with a flat…

We make some remarks about bubbling on, not necessarily proper, champs de Deligne-Mumford, i.e. compactification of the space of mappings from a given (wholly scheme like) curve, so, in particular, on quasi-projective projective varieties.…

In the spirit of the geometric approach to two-dimensional conformal field theory, we explicitly associate to every holomorphic vertex operator algebra a section of a power of Hodge line bundle on the moduli space of curves of arbitrary…

Let $X$ be a completely regular space. For a non-vanishing self-adjoint Banach subalgebra $H$ of $C_B(X)$ which has local units we construct the spectrum $\mathfrak{sp}(H)$ of $H$ as an open subspace of the Stone-Cech compactification of…

We extend the results of our paper "Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0" written with Laure Saint-Raymond to the case of forced linear wave equations in any dimension. We prove that, in dimension…

We prove a semisimplicity result for the boundary, in the corresponding Deligne-Mumford compactification, of a totally geodesic subvariety of a moduli space of Riemann surfaces. At the level of Teichm\"uller space, this semisimplicity…

We give an integrability criterion for a projective limit of Banach distributions on a Fr\'echet manifold which is a projective limit of Banach manifolds. This leads to a result of integrability of projective limit of involutive bundles on…

We prove a semi-invertible Oseledets theorem for cocycles acting on measurable fields of Banach spaces, i.e. we only assume invertibility of the base, not of the operator. As an application, we prove an invariant manifold theorem for…