Related papers: The Manin conjecture in dimension 2

Recent developments in our understanding of neutrino masses and their implications for physics beyond the standard model are reviewed.

The current status of neutrino physics is reviewed with some near future perspective. After recollecting the birth of modern neutrino physics with nonzero masses and flavor mixing, I summarize the present status of measurement of the mixing…

We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1.

This is a survey paper on Geometric Manin's conjecture which was proposed by Brian Lehmann and the author. We introduce Geometric Manin's conjecture (GMC) and review some recent progress on this conjecture.

In this paper, we confirm the Fino-Vezzoni Conjecture for unimodular Lie algebras which contain abelian ideals of codimension two, a natural generalization to the class of almost abelian Lie algebras. This provides new evidence towards the…

In connection to the development of the field of Combinatorics on Words, we present a list of open problems and conjectures that were stated during the ten last meetings WORDS. We wish to continually update the present document by adding…

This memoire consists of two main results. In the first one we describe Ricci flow theory and we give an educative way for proving Elliptization Conjecture and then we prove Poincare conjecture which is the second proof of Perelman for…

Artin's conjecture is established for all forms that can be realised as a diagonal form on an hyperplane.

In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…

We produce new examples of Riemannian manifolds with scalar curvature lower bounds and collapsing behavior along codimension 2 submanifolds. Applications of this construction are given, primarily on questions concerning the stability of…

This brief survey deals with multi-dimensional Diophantine approximations in sense of linear form and with simultaneous Diophantine approximations. We discuss the phenomenon of degenerate dimension of linear subspaces generated by the best…

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

It is shown that the Ramadanov conjecture implies the Cheng conjecture. In particular it follows that the Cheng conjecture holds in dimension two.

These lecture notes give an introduction to the Brauer-Manin obstruction to the existence of rational points, focusing on the interplay between theory and computation.

This paper explores special conditions on the starting value of a Collatz sequence which imply that the Collatz conjecture is true. This is the result of the collaboration of a retired mathematics professor (Koelzer) and a retired physics…

These lecture notes discuss classical models of liquid crystals, and the different ways in which defects are described according to the different models.

In the last two decades experiments have established the existence of neutrino oscillations and most of the related parameters have by now been measured with reasonable accuracy. These results have accomplished a major progress for particle…

We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.

Bi-large patterns for the leptonic mixing matrix are confronted with current neutrino oscillation data. We analyse the status of these patterns and determine, through realistic simulations, the potential of upcoming long-baseline experiment…

We prove that every del Pezzo surface of degree two over a finite field is unirational, building on the work of Manin and an extension by Salgado, Testa, and V\'arilly-Alvarado, who had proved this for all but three surfaces. Over general…