Related papers: The mathematization of the individual sciences - r…
This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. The purpose of our…
The growth of cities has traditionally been studied from a population perspective, while urban expansion-its spatial growth-has often been approached qualitatively. However, characterizing and modeling this spatial expansion is crucial,…
The workshop `Astrophysical Dynamics 1999/2000' followed a homonymous advanced research course, and both activities were organized by me. In this opening paper of the proceedings book, I describe them and document their strong impact on the…
We discuss a recent line of research investigating inverse theorems with respect to general k-wise correlations, and explain how such correlations arise in different contexts in mathematics. We outline some of the results that were…
Talk given at ICM '98, Berlin, reviewing some of the recent developments in understanding of string theory for a mathematical audience (to appear in Documenta Mathematica).
This article presents an in-depth educational overview of the latest mathematical developments in coupled cluster (CC) theory, beginning with Schneider's seminal work from 2009 that introduced the first local analysis of CC theory. We offer…
This is an overview article. In his Habilitationsvortrag, Riemann described infinite dimensional manifolds parameterizing functions and shapes of solids. This is taken as an excuse to describe convenient calculus in infinite dimensions…
Data science methodologies, which have undergone significant developments recently, provide flexible representational performance and fast computational means to address the challenges faced by traditional scientific methodologies while…
This is in some sense an addendum to the book Relational Mathematics by the first-named author. It originated from work on diverse other topics during which a lot of purely relational results with broad applicability have been produced.…
Remarks at the Irving Kaplansky Memorial about a collaboration during the early period of the renewal of contacts between mathematicians and theoretical physicists.
These are the proceedings of the workshop "Math in the Black Forest", which brought together researchers in shape analysis to discuss promising new directions. Shape analysis is an inter-disciplinary area of research with theoretical…
Research in cosmology traditionally divided into two separate lines. On the one hand was the search for initial conditions: the cosmological parameters H, Omega, Omega_b, and Lambda, and the power spectrum P(k). On the other hand was the…
Submitted to F. Schweitzer (ed.), Microscopic Models for Economic Dynamics, Lecture notes in physics, Springer, Berlin-Heidelberg 2002.kiel.tex
We stand at the foot of a significant inflection in the trajectory of scientific discovery. As society continues on its fast-paced digital transformation, so does humankind's collective scientific knowledge and discourse. We now read and…
Here we review a kind of post-World-War-II "Nachtrag" to H. Weyl's philosophical comments on mathematics and the natural sciences published in the middle of the 1920s. In a talk given at Z\"urich in the late 1940s, Weyl discussed…
This paper surveys the significant progress over the past couple of decades in the theory of stratified spaces through the application of controlled methods as well as through the application of intersection homology.
I propose a broad, multi-dimensional conception of altmetrics, namely as traces of the computerization of the research process. Computerization should be conceived in its broadest sense, including all recent developments in ICT and…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
Scientometrics is the field of quantitative studies of scholarly activity. It has been used for systematic studies of the fundamentals of scholarly practice as well as for evaluation purposes. Although advocated from the very beginning the…
In the last two decades recurrence plots (RPs) were introduced in many different scientific disciplines. It turned out how powerful this method is. After introducing approaches of quantification of RPs and by the study of relationships…