Related papers: A survey on Seifert fiber space conjecture
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
We show that discretization of spacetime naturally suggests discretization of Hilbert space itself. Specifically, in a universe with a minimal length (for example, due to quantum gravity), no experiment can exclude the possibility that…
We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.
We investigate a stronger formulation of Webb's conjecture on the contractibilty of the orbit space of the p-subgroup complexes in terms of finite topological spaces. The original conjecture, which was first proved by Symonds and, more…
Given a relatively minimal non locally trivial fibred surface f: S->B, the slope of the fibration is a numerical invariant associated to the fibration. In this paper we explore how properties of the general fibre of $f$ and global…
I give a simplified proof of one of the main results in the recent preprint arXiv:1311.5858 by X. Luo and K. Zuo. Furthermore, I discuss the relation with the Coleman-Oort conjecture on special curves in the Torelli locus.
We prove several extensions of the Erdos-Fuchs theorem.
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
In this paper we adopt a geometric point of view regarding a famous conjecture due to Littlewood in diophantine approximation of real numbers. Following the spirit of the geometric theory of continued fractions, we give a sufficient…
The Fourier extension conjecture of E. Stein was proved in the plane in 1970 by C. Fefferman, see also Zygmund and Carleson and Sj\"olin, with simplifications given by other authors later on, in particular by L. H\"ormander and T. Tao. We…
We propose a conjectural extension to positive characteristic case of a well known Deligne's theorem on the existence of super fiber functors. We prove our conjecture in the special case of semisimple categories with finitely many…
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
In this note, we prove that every fibre space structures of a projective irreducible symplectic manifold is a lagrangian fibration.
Inspired by the quantitative $K$-theory, in this paper, we introduce the coarse Baum-Connes conjecture with filtered coefficients which generalizes the original conjecture. There are two advantages for the conjecture with filtered…
Any leafwise connection on a fibre bundle over a foliated manifold is proved to come from a connection on this fibre bundle.
We survey the state of the union-closed sets conjecture.
We survey Kondrat'ev--Landis' conjecture, providing an up-to-date account of the main advances and describing the techniques developed. We complement the overview with references and formulations of the problem in further closely connected…
We propose generalized Fermat's conjecture in the framework of arithmetic dynamics, and give evidences. The multi-indexed version is added.
In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…
We formulate several conjectures on mean convex domains in the Euclidean spaces, as well as in more general spaces with lower bonds on their scalar curvatures, and prove a few theorems motivating these conjectures.