Related papers: An Extension of Mok's Theorem on the Generalized F…

We investigate Koszul cohomology on irreducible nodal curves. In particular, we prove both Green and Green-Lazarsfeld conjectures for the general k-gonal nodal curve.

We show that contracting self-similar groups satisfy the Farrell-Jones conjectures as soon as their universal contracting cover is non-positively curved. This applies in particular to bounded self-similar groups. We define, along the way, a…

The conjecture of Masser-Oesterl\'e, popularly known as $abc$-conjecture have many consequences. We use an explicit version due to Baker to solve a number of conjectures.

A theorem due to Ohkawa states that the collection of Bousfield equivalence classes of spectra is a set. We extend this result to arbitrary combinatorial model categories.

Using the notion of generalized divisors introduced by Hartshorne, we adapt the theory of adjoint forms to the case of Gorenstein curves. We show an infinitesimal Torelli-type theorem for vector bundles on Gorenstein curves. We also…

In this paper we use the strength of the constraint method in combination with a generalized Borsuk-Ulam type theorem and a cohomological intersection lemma to show how one can obtain many new topological transversal theorems of Tverberg…

In the paper, we generalize the Arzel\`a-Ascoli theorem in the setting of uniform spaces. At first, we recall well-known facts and theorems coming from monographs of Kelley and Willard. The main part of the paper introduces the notion of…

In this paper we formulate a conjecture which is a strengthening of an extension theorem of Bakonyi and Timotin for positive definite functions on the free group on two generators. We prove that this conjecture implies Connes' embedding…

In this note we propose a generalisation of Seymour's Second Neighbourhood Conjecture to two directed graphs on a vertex set. We prove that this generalisation holds in the case of tournaments, and we show that a natural strengthening of…

A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight function depending on two integers. For a…

The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed…

Our main goal in this article is to prove a new extension theorem for sections of the canonical bundle of a weakly pseudoconvex K\"ahler manifold with values in a line bundle endowed with a possibly singular metric. We also give some…

In this paper, we develop a new index theory for manifolds with polyhedral boundary. As an application, we prove Gromov's dihedral extremality conjecture regarding comparisons of scalar curvatures, mean curvatures and dihedral angles…

In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…

We present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk-Ulam theorem perspective.

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant…

A generalization of the Hartogs theorem is proved for a class of Tubes structures. We assume that the intervening commutative Lie algebra admits at least a number of globally solvable generators greater or equal to the structure…

We prove a continued fraction expansion for a certain q--tangent function that was conjectured by Prodinger.

We show that if there exists a counter example for the rational case of the Franks-Misiurewicz conjecture, then it must exhibit unbounded deviations in the complementary direction of its rotation set.

We disprove a conjecture of Frank stating that each weakly 2k-connected has a k-vertex-connected orientation. For k at least 3, we also prove that the problem of deciding whether a graph has a k-vertex-connected orientation is NP-complete.