Related papers: Progress in number theory in the years 1998-2009

We summarize progress made in theoretical astrophysics and cosmology over the past decade and areas of interest for the coming decade. This Report is prepared as the TF09 "Astrophysics and Cosmology" topical group summary for the Theory…

Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of…

This chapter surveys the advances of the past decade arising from the contributions of Indian mathematicians in the broad areas of operator algebras and operator theory. It brings together the work of twenty mathematicians and their…

The results summarized here are intended as rigorous mathematical statements on various physical models coming from condensed matter physics, statistical mechanics (classical and quantum), quantum field theory and cold atoms physics. The…

In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also…

We survey recent developments on the Restriction conjecture.

We give a proposal for future development of the model theory of valued fields. We also summarize some recent results on p-adic numbers.

The concept of number and its generalization has played a central role in the development of mathematics over many centuries and many civilizations. Noteworthy milestones in this long and arduous process were the developments of the real…

We first review the historical developments, both in physics and in mathematics, that preceded (and in some sense provided the background of) deformation quantization. Then we describe the birth of the latter theory and its evolution in the…

We discuss the recent results obtained in the context of PDF determination with the inclusion of logarithmic resummations and their phenomenological applications.

74 new integer sequences are introduced in number theory, and for each of them is given a characterization, followed by open problems. each one a general question: how many primes each sequence has.

We survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies. We do not attempt to be exhaustive but try instead to give some personal interpretations and some research directions.…

This article surveys some of the highlights in the development of string theory through the first superstring revolution in 1984. The emphasis is on topics in which the author was involved, especially the observation that critical string…

I describe our understanding of physics near the Planck length, in particular the great progress in the last four years in string theory. These are lectures presented at the 1998 SLAC Summer Institute.

Probably we have observed a new simple phenomena dealing with approximations to two real numbers.

I report on recent theoretical developments at Quark Matter 2006.

There have been many remarkable developments in our understanding of superstring theory in the past few years, a period that has been described as ``the second superstring revolution.'' Several of them are discussed here. The presentation…

The purpose of this article is to review the achievements made in the last few years towards the understanding of the reasons behind the success and subtleties of neural network-based machine learning. In the tradition of good old applied…

This is a survey article describing some recent results at the interface of homogeneous dynamics and Diophantine approximation.

One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.