Related papers: Counterexamples of the Geometrization Conjecture

In this paper, the abc conjecture is negated under certain conditions

We prove a uniformization theorem in complex algebraic geometry.

We introduce a generalization of the b-metric we call a (b,c)-metric. We show that if $X$ is a $(b,c)$-metric space and $\psi: X \longrightarrow Y$ is a quasi-isometry then $Y$ is $(b,c)$-metrizable. We also define a particular kind of…

We survey on algebraically elliptic varieties in the sense of Gromov.

We provide explicit counterexamples to the so-called Complement Problem in every dimension $n\geq3$, i.e. pairs of non-isomorphic irreducible hypersurfaces $H_1, H_2\subset\mathbb{C}^{n}$ whose complements $\mathbb{C}^{n}\setminus H_1$ and…

We formulate a relative, representation theoretic, notion of the algebraic cone construction. This motivates a generalization of the cone corresponding to a preprojective algebra.

A covariant functor on the elliptic curves with complex multiplication is constructed. The functor takes values in the noncommutative tori with real multiplication. A conjecture on the rank of an elliptic curve is formulated.

This supplementary part of the paper gr-qc 9312038 contains the necessary proofs of the claims stated in the main part.

Three complementation-like involutions are constructed on permutations to prove, and in some cases generalize, all remaining fourteen joint symmetric equidistribution conjectures of Lv and Zhang. Further enumerative results are obtained for…

We give a minimal counterexample for a conjecture of Ross and Yong (2015) which proposes a K-Kohnert rule for Grothendieck polynomials. We conjecture a revised version of this rule. We then prove both rules hold in the $321$-avoiding case.

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

We discuss applications of minimal surfaces to comparison geometry.

In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We first motivate this diophantine problem, prove some results, provide a number of interesting examples and, finally…

We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof…

In this paper we make some observations concerning m-metric spaces and point out some discrepancies in the proofs found in the literature. To remedy this, we propose a new topological construction and prove that it is in fact a…

We propose several Hodge theoretic analogues of the conjectures of Hopf and Singer, and prove them in some special cases.

We introduce the notion of geometric pseudo-quantisation based on geometric quantisation with a weakened curvature condition. We show how such a structure arises naturally from simple deformations of the symplectic structure and pullbacks…

Given two irreducible curves of the plane which have isomorphic complements, it is natural to ask whether there exists an automorphism of the plane that sends one curve on the other. This question has a positive answer for a large family of…

In this expository note, we give a self-contained introduction to some modern incarnations of Hamiltonian reduction. Particular emphasis is placed on applications to symplectic geometry and geometric representation theory. We thereby…

We disprove a conjecture in Density Functional Theory, relative to multimarginal optimal transport maps with Coulomb cost. We also provide examples of maps satisfying optimality conditions for special classes of data.