Related papers: The Manin conjecture in dimension 2

We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…

This article is a continuation of my previous paper on miraculous pentagrams published in Annales Scientifiques de Facult\'e des Sciences de Toulouse in 2013. We discuss the moduli space of miraculous pentagrams which is the Del Pezzo…

We present a new conjecture for the $SU_q(N)$ Perk-Schultz models. This conjecture extends a conjecture presented in our article (Alcaraz FC and Stroganov YuG (2002) J. Phys. A vol. 35 pg. 6767-6787, and also in cond-mat/0204074).

In this talk I review our present knowledge on neutrino masses and mixing trying to emphasize the most direct implications and challenges of these results.

This is an informal write up of my talk in Berlin. It gives some background to Goddard's talk (math.QA/9808136) about the moonshine conjectures.

These lecture notes discuss methods, recent results and future prospects in proton-proton physics at the Large Hadron Collider.

In this paper we study the lattice point covering property of some regular polygons in dimension 2.

In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.

We introduce the split torsor method to count rational points of bounded height on Fano varieties. As an application, we prove Manin's conjecture for all nonsplit quartic del Pezzo surfaces of type $\mathbf A_3+\mathbf A_1$ over arbitrary…

In this note, we give some new families of two-stage spaces for which the torus rank conjecture is affirmed.

Current evidence for neutrino oscillation is reviewed, some areas for closer investigation are suggested, and a plausible future experimental program is summarized.

In 2007, Dmytrenko, Lazebnik and Williford posed two related conjectures about polynomials over finite fields. Conjecture~1 is a claim about the uniqueness of certain monomial graphs. Conjecture~2, which implies Conjecture~1, deals with…

Status of the problem of neutrino masses, mixing and oscillations is discussed. Future perspectives are briefly considered.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

We derive the expressions for the local, on-shell closed co-dimension 2 forms in the Palatini formulation of general relativity and explicitly show their on-shell equivalence to those of the metric formulation. When compared to other first…

In the first two of these lectures, I present the evidence for baryonic dark matter and describe possible forms that it may take. The final lecture discusses formation of baryonic dark matter, and sets the cosmological context.

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…

We develop a strategy to classify the components of the space of sections of a del Pezzo fibration over $\mathbb{P}^{1}$. In particular, we prove the Movable Bend and Break lemma for del Pezzo fibrations. Our approach is motivated by…

This is an exposition of recent developments in the theory of bounded differences between primes. Readers are expected to be beginners of analytic number theory. The present text is a substantially improved and augmented version of the one…

We prove a version of Manin's conjecture (over $\mathbb{F}_{q}$ for $q$ large) and the Cohen--Jones--Segal conjecture (over $\mathbb{C}$) for maps from rational curves to split quartic del Pezzo surfaces. The proofs share a common method…