Related papers: Progress in number theory in the years 1998-2009
This is a brief overview of some turning points in the history of infinitesimals.
This is a summary talk covering recent progress in perturbative methods for gauge theories and gravity, applications of AdS/CFT duality, vacuum energy, and string theory models of particle physics and cosmology.
A comprehensive review on Cook's contribution in the theory of NP-Completeness with relations to modern mathematics.
The possibility of quantum computing has been proposed decades ago, at least as far back as the 1980s, and distributed quantum computing has been studied around two decades ago. Recent times have seen experimental successes and advances in…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
This is a survey of old and new problems and results in additive number theory.
An assessment is offered of the progress that the major approaches to quantum gravity have made towards the goal of constructing a complete and satisfactory theory. The emphasis is on loop quantum gravity and string theory, although other…
Text summarization research has undergone several significant transformations with the advent of deep neural networks, pre-trained language models (PLMs), and recent large language models (LLMs). This survey thus provides a comprehensive…
The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, approximation theory worked as a…
The main purpose of this survey is to introduce an inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic…
Expansion of real numbers is a basic research topic in number theory. Usually we expand real numbers in one given base. In this paper, we begin to systematically study expansions in multiple given bases in a reasonable way, which is a…
Inspired by computer assisted proofs in analysis, we present an interval approach to real-number computations.
The current state of cosmology is easy to summarize: a very successful standard model -- the hot big-bang cosmology -- that accounts for the evolution of the Universe from 10^{-2} sec until the present; bold ideas based upon early-Universe…
We review the current standard model for the evolution of cosmic structure, tracing its development over the last forty years and focusing specifically on the role played by numerical simulations and on aspects related to the nature of dark…
We review recent progress in the experimental knowledge of and theoretical speculations about nucleon form factors, with special emphasis on the large Q2 region.
We review an information-theoretic approach to quantum cosmology, summarising the key results obtained to date, including a suggestion that an accelerating universe will eventually turn around.
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
The study of undecidability in problems arising from physics has experienced a renewed interest, mainly in connection with quantum information problems. The goal of this review is to survey this recent development. After a historical…
Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from…
We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known…