Related papers: Hans Grauert: Mathematician Pur
Schmidt games and the Cantor winning property give alternative notions of largeness, similar to the more standard notions of measure and category. Being intuitive, flexible, and applicable to recent research made them an active object of…
This essay, an excerpt of the author's Ph.D. in Philosophy of mathematics (2012) thought of as being a companion to recent discoveries of new explicit Cartan geometry curvatures, analyzes how Gauss, after having devised the isometrically…
I present my viewpoint on complexity, stressing general arguments and using a rather simple language.
This is an introduction of the volume of the journal Commentationes Mathematicae Universitatis Caroalinae dedicated to the memory of V\v{e}ra Trnkov\'a}.
This is a survey article about some of the work of Peter Scholze for the Jahresbericht der DMV. No originality is claimed. It is hoped that it can serve as a guideline to an exciting and increasingly large edifice of theory.
Prof. K.G Ramanathan was a legendary Indian Mathematician, working in Number Theory and a prolific Institution builder. Apart from this, he was an excellent teacher and influenced several brilliant students. In this article, we overview his…
Algebraic computing in relativity and gravitation dates back more than thirty years, but only relatively recently has hardware of sufficient power to tackle large scale calculations become commonplace. Whereas it is generally understood…
A fundamental property of compact groups and compact quantum groups is the existence and uniqueness of a left and right invariant probability -- the Haar measure. This is a natural playground for classical and quantum probability, provided…
Lecture given before the Royal Academy Vienna that summarizes the state of knowledge about the mathematics of the ancient Egyptians, up to 1884. Contains all relevant references to classical Greek texts, and the 'latest' archeology results.…
This is a comment on a collection of statements gathered on the occasion of the Quantum Physics of Nature meeting in Vienna.
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 paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…
Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction…
I provide some comments on Arithmetic Teichmuller Spaces constructed in my paper arXiv:2106.11452.
Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is…
"I am an industrial mathematician." When asked to identify my profession or academic field of study, this is the most concise answer I can provide. However, this seemingly straightforward statement is commonly greeted by a blank stare or an…
This is a preliminary version of the textbook on integrable systems. The work has been partly supported by Grant Nr.10/2006-RU, Austrian Academic Exchange Service \"OAD and Grant P20164-N18, Austrian Science Fund FWF
This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.
This is a brief overview of the role of mathematicians in the so-called "Luzin Case" as well as some analysis of the mathematical and humanitarian roots of the affair.
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.