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We study the moduli space of logarithmic connections of rank $2$ on $\mathbb{P}^1 \setminus \{ t_1, \dots, t_5 \}$ with fixed spectral data. The aim of this paper is to compute the cohomology of such space, and this computation will be used…

We give a proof of the existence of radial (smooth) parallel sections of vector bundles endowed with a linear connection.

We study the space of "link maps": the space of maps of a disjoint union of compact, closed manifolds P_1, . . ., P_k into a manifold N whose images are pairwise disjoint. We apply the manifold calculus of functors developed by Goodwillie…

In this paper, we study certain moduli spaces of vector bundles on the blowup of the projective plane in at least 10 very general points. Moduli spaces of sheaves on general type surfaces may be nonreduced, reducible and even disconnected.…

We present some remarks about the embedding of spaces of Schwartz distributions into spaces of Colombeau generalized functions. We show that the various constructions of such embeddings existing in the literature lead in fact to the same…

We compute all the simply connected homogeneous and infinitesimally homogeneous surfaces admitting one or more invariant affine connections. We find exactly six non equivalent simply connected homogeneous surfaces admitting more than one…

Given a point configuration A, we uncover a connection between polynomial-reproducing spline spaces over subsets of conv(A) and fine zonotopal tilings of the zonotope Z(V) associated to the corresponding vector configuration. This link…

It is a result of Gruson and Peskine that the invariants of a set points in $\ptwo$ in general position are connected. Associated to a space curve there are sequences of invariants which generalize the invariants of points in $\ptwo$. The…

Given a perversity function in the sense of intersection homology theory, the method of intersection spaces assigns to certain oriented stratified spaces cell complexes whose ordinary reduced homology with real coefficients satisfies…

We compute the equivariant cohomology of smooth Calogero-Moser spaces and some associated symplectic resolutions of symplectic quotient singularities.

In this paper we give some coupled fixed point results for mappings satisfying different contractive conditions on complete partial metric spaces.

Given an acyclic map $X\to Y$ of closed manifolds dimension $d$, we study the relationship between the embeddings of $Y$ in $S^{n}$ with those of $X$ in $S^{n}$ when $n-d \ge 3$. The approach taken here is to first solve the Poincar\'e…

We show that the moduli space of $n$ suitably embedded copies of a closed smooth manifold $P$ inside a closed smooth manifold $M$ satisfies cohomological periodicity over $\mathbb F_\ell$ when $n$ grows, with an explicit linear bound on the…

We establish inequalities that constrain the genera of smooth cobordisms between knots in 4-dimensional cobordisms. These "relative adjunction inequalities" improve the adjunction inequalities for closed surfaces which have been…

We show that every locally flat topological embedding of a 3-manifold in a smooth 5-manifold is homotopic, by a small homotopy, to a smooth embedding. We deduce that topologically locally flat concordance implies smooth concordance for…

We present a complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion, extending previously known results in the literature. Consequently, we also establish a splitting theorem for compact manifolds…

Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…

We describe the equivariant cohomology ring of rationally smooth projective embeddings of reductive groups. These embeddings are the projectivizations of reductive monoids. Our main result describes their equivariant cohomology in terms of…

We show a correspondence between the set of all G-invariant projectively flat connections on a homogeneous apace $M=G/K$, and the one of all {G}^~-invariant flat connections on a homogeneous space {M}^~={G}^~/K, where {G}^~ is a central…

Any moduli space of representations of a quiver (possibly with oriented cycles) has an embedding as a dense open subvariety into a moduli space of representations of a bipartite quiver having the same type of singularities. A connected…