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

This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the…

The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…

Some recent results in supersymmetric grand unified theories are reviewed.

In this presentation, I will summarize the present status of the developments with a Universal Theory of Relativity \cite{smw-utr}. Some general challenges to be overcome will also be discussed.

Over the past two decades, the field of high-dimensional statistics has experienced substantial progress, driven largely by technological advances that have dramatically reduced the cost and effort for data collection and storage across a…

Uniquely among the sciences, quantum cryptography has driven both foundational research as well as practical real-life applications. We review the progress of quantum cryptography in the last decade, covering quantum key distribution and…

Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is…

The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…

We summarize some of the main ideas and results around symplectic field theory, from its early inception up to recent and ongoing developments.

This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…

Numerical relativity has made big strides over the last decade. A number of problems that have plagued the field for years have now been mostly solved. This progress has transformed numerical relativity into a powerful tool to explore…

The goal of this annotated bibliography is to record every publication on the topic of comparative prime number theory (through mid-2024) together with a summary of its results. We use a unified system of notation for the quantities being…

This article summarizes the process by which astronomers and astrophysicists reached a consensus view as to what are the highest priority scientific projects for the decade of the 1990s. I also review the remarkable success of these…

Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM

We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…

We summarise the main results from a number of our recent articles on the subject of probabilistic temperature forecasting.

In this talk, I review progress in experimental QCD in the last year, concentrating on the results and phenomenology of the first year of running of the LHC.

There has been a remarkable increase in work at the interface of computer science and game theory in the past decade. In this article I survey some of the main themes of work in the area, with a focus on the work in computer science. Given…

The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.

We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.