Related papers: Branko Gr\"unbaum in many dimensions
In a classic paper Schr\"oder posed four combinatorial problems about the number of certain types of bracketings of words and sets. Here we address what these bracketings look like on average. For each of the four problems we prove that a…
This article gives a comprehensive review on thick brane solutions and related topics. Such models have attracted much attention from many aspects since the birth of the brane world scenario. In many works, it has been usually assumed that…
In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.
I argue that GR Cauchy and Initial Value Problem mathematics is a valuable source of ideas for braneworlds based on higher-dimensional Einstein field equations.
A portrait of Kurt Goedel with emphasis on his work on relativity theory and idealistic philosophy.
The paper proposes open problems in classical Kolmogorov complexity. Each problem is presented with background information and thus the article also surveys some recent studies in the area.
This note describes some open problems that can be examined with the purpose of gaining additional insight of how to solve the problem of finding a general classification of geodetic graphs
Brane-world models, where observers are restricted to a brane in a higher-dimensional spacetime, offer a novel perspective on cosmology. I discuss some approaches to cosmology in extra dimensions and some interesting aspects of gravity and…
Quantum graphs have become in this century a favorite playground for mathematicians, mathematical physicists, and chemists, due to their manifold applications as models of thin structures, as well as presenting sometimes simpler playground…
Brane-Universe model embedded in 6-dimensional space-time with the signature (2+4) is considered. A matter is gravitationally trapped in three space dimensions, but both time-like directions are open. Choosing of the dimension and the…
This is an English translation of "The Resolvent Problem" by Tschebotarow/Chebotarev. In this article, Chebotarev summarizes the history of the resolvent problem from compass and ruler constructions to Klein and Hilbert' formlutions of the…
We introduce and study properties of certain new harmonic function spaces on products of upper half-spaces.Norm estimates for the so-called expanded Bergman projections are obtained.Sharp theorems on multipliers acting on certain Sobolev…
In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that…
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.
A geometric theory of brane-worlds with large or non-compact extra dimensions is presented. It is shown that coordinate gauge independent perturbations of the brane-world correspond to the Einstein-Hilbert dynamics derived from the…
The paper addresses the existence of multi-bubble solutions for the well-known Brezis-Nirenberg problem. Although there is extensive literature on the subject, the existence of solutions that blow up at multiple points in a 4D bounded…
We discuss some open problems in the Geometry of Banach spaces having Ramsey-theoretic flavor. The problems are exposed together with well known results related to them.
Current attempts to find a unified theory that would reconcile Einstein's General Relativity and Quantum Mechanics, and explain all known physical phenomena, invoke the Kaluza-Klein idea of extra spacetime dimensions. The best candidate is…
This is a brief survey of recent works by Neil Trudinger and myself on the Bernstein problem and Plateau problem for affine maximal hypersurfaces.