Related papers: Progress in number theory in the years 1998-2009
Mathematical aspects of contemporary classical and quantum gauge theory are sketched.
Nuclear theory today aims for a comprehensive theoretical framework that can describe all nuclei. I discuss recent progress in this pursuit and the associated challenges as we move forward.
A summary of QCD results obtained at e+e- experiments in recent years is given. Emphasis is put on basic QCD tests and \alpha_s measurements with event shapes.
The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot based data analysis and to widen its application potential. We will give a brief overview about important and…
This is an introduction to some recent developments in string theory and M theory. We try to concentrate on the main physical aspects, and often leave more technical details to the original literature.
We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…
Numerical relativity is finally approaching a state where the evolution of rather general (3+1)-dimensional data sets can be computed in order to solve the Einstein equations. After a general introduction, three topics of current interest…
We survey selected developments in the metric geometry of the space of K\"ahler metrics, emphasizing results from the past decade, highlighting open problems along the way.
An introductory guide to mathematical cosmology is given focusing on the issue of the genericity of various important results which have been obtained during the last thirty or so years. Some of the unsolved problems along with certain new…
The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
We are emerging from a period of consolidation in particle physics. Its great, historic achievement was to establish the Theory of Matter. This Theory will serve as our description of ordinary matter under ordinary conditions -- allowing…
An overview of some of the developments in string theory over the past two years is given, focusing on four topics: realistic (standard model like) models from string theory, geometric engineering and theories with fluxes, the gauge…
We study how well a real number can be approximated by sums of two or more rational numbers with denominators up to a certain size.
Quantum computational advantage was claimed for the first time in 2019 and several experiments since then have reinforced the claim. And yet, there is no consensus whether or not quantum advantage has actually been achieved. In this…
This is Chapter 1 in the book General Relativity and Gravitation: A Centennial Perspective, Edited by Abhay Ashtekar (Editor in Chief), Beverly Berger, James Isenberg, Malcolm MacCallum. Publisher: Cambridge University Press (June, 2015).…
We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
Selected theoretical developments in neutrino-nucleus scattering in 2015-2016 are reviewed.
In the past few decades there has been a good deal of papers which are concerned with optimization problems in different areas of mathematics (along 0-1 words, finite or infinite) and which yield - sometimes quite unexpectedly - balanced…
We give a short review of recent progress on the positive energy theorem in general relativity, especially for spacetimes with nonzero cosmological constant.