Related papers: Progress in number theory in the years 1998-2009
The notion of $\tau$-tilting theory was introduced by Adachi, Iyama and Reiten at the beginning of the last decade and quickly became one of the most active areas of research in the representation theory of finite dimensional algebras. The…
Number theory as a coherent mathematical subject started with the work of Fermat in the decade from 1630 to 1640, but modern number theory, that is, the systematic and mathematically rigorous development of the subject from fundamental…
Research on the development of science has focused on the creation of multidisciplinary teams. However, while this coming together of people is symmetrical, the ideas, methods, and vocabulary of science have a directional flow. We present a…
An outline of J\"org Eschmeier's main mathematical contributions is organized both on a historical perspective, as well as on a few distinct topics. The reader can grasp from our essay the dynamics of spectral theory of commutative tuples…
This article traces the development of fluctuation theory and its deep connection to irreversibility, from equilibrium to near-equilibrium, and finally to far-from-equilibrium systems. Classical fluctuation theorems, which capture the…
We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog…
The final (third) part of the theory gives the results of numerical calculations according to the formulas derived in the previous two parts. Also the comparison with the already published theories is given. Some conclusions connected with…
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…
In this paper we provide an exhaustive survey of the current state of the mathematics of filtration enlargement and an interpretation of the key results of the literature from the viewpoint of mathematical finance. The emphasis is on…
This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification. While there has been substantial progress across all areas of control, the theory…
This article gives an overview, aimed at theoretical particle physicists, of some recent developments in cosmology.
We present a partial survey on normal numbers, including Keane's contributions, and with recent developments in different directions.
The purpose of this book is to provide an introduction to period theory and then to place it within the matrix of recursive function theory.
A Letter to the Editor shortly summing up ten or so years of research into the h-index.
Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.
This is a survey on special metrics. We shall present some results and open questions on special metrics mainly appeared in the last 10 years
I shortly review time period of twelve years, 1989-2000, which was devoted to a theoretical support of experiments at LEP and SLC at Z resonance and discuss several directions of possible future work in the field of precision theoretical…
We retrace the recent history of the Umbral Calculus. After studying the classic results concerning polynomial sequences of binomial type, we generalize to a certain type of logarithmic series. Finally, we demonstrate numerous typical…
After briefly reviewing basic concepts of perturbative string theory, we explain in simple terms some of the new findings that created excitement among the string physicists. These developments include non-perturbative dualities and a…