Related papers: The Manin conjecture in dimension 2
Let S Q denote x 3 = Q(y 1 ,. .. , y m)z where Q is a primitive positive definite quadratic form in m variables with integer coefficients. This S Q ranges over a class of singular cubic hypersurfaces as Q varies. For S Q we prove (i)…
We present a pedagogical review of neutrino physics. In the first lecture we describe the theoretical motivation for neutrino masses, and explain how neutrino flavor oscillation experiments can probe neutrino masses. In the second lecture…
Several results about the union-closed sets conjecture are presented.
Recent evidence for neutrino oscillations has revolutionized the study of neutrino masses and mixing. This report gives an overview of what we are learning from the neutrino oscillation experiments, the prospects for the near term, and the…
We establish a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces. M-theory on T^k corresponds to P^2 blown up at k generic points; Type IIB corresponds to P^1\times P^1. The moduli of compactifications of…
We survey the state of the union-closed sets conjecture.
The present note sketches a theory of constructs.
These are the expanded and detailed notes of the lectures given by the authors during the school and workshop entitled "Liaison and Related Topics," held at the Politecnico di Torino during the period October 1-5, 2001. In these notes we…
Introductory lectures notes on cosmology, aimed at master students in physics and based on a course held at Milano University (in Italian).
Some aspects of the current neutrino oscillation phenomenology are briefly discussed, with emphasis on the status of mass-mixing parameters relevant for scenarios with three active neutrinos, and with an additional fourth sterile neutrino.
In this talk, some aspects of duality symmetries are presented.
In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree 2.
The first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \cite{I} and numerous applications in \cite{RS} and \cite{Y2}.…
These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and Hamiltonian systems. They are based on a series of lectures given by the author at Universit\`a degli Studi di Napoli "Federico II" (April 2009), at…
In this note we discuss the possibility to get a time rather than space in the scenario of (de)construction of new dimension.
We compute a naturally defined measure of the size of the nef cone of a Del Pezzo surface. The resulting number appears in a conjecture of Manin on the asymptotic behavior of the number of rational points of bounded height on the surface.…
A summary of the present experimental status of meson physics is presented. The presentation includes the new results presented at the MESON06 workshop, as well as other recent experimental developments in the field.
The field of neutrino physics is currently very exciting, with several recent results pointing to new physics. I will give an overview of the current experimental situation, focusing primarily on neutrino oscillation results. The data are…
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…
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.