Related papers: Branko Gr\"unbaum in many dimensions
This is a structured compilation of some of my favourite open problems.
In 2023, H.\,Brezis published a list of his ``favorite open problems", which he described as challenges he had ``raised throughout his career and has resisted so far". We provide a complete resolution to the first one--Open Problem 1.1--in…
This paper is a collection of thoughts and observations, being partly a review and partly a report of current research, on recent work in various aspects of Gr\"unbaum colorings, their existence and usage. In particular, one of the most…
This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season…
This is a collection of open problems in geometry that I think of as puzzles: they stick to my brain -- I see many grips, but no spare hands. Puzzle-charm is the only criterion for including a problem here; importance is ignored.
The paper attempts to describe the space of possible mind designs by first equating all minds to software. Next it proves some interesting properties of the mind design space such as infinitude of minds, size and representation complexity…
An open problem concerning Riemann sums, posed by O. Furdui, is considered.
This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…
The present article is devoted to the description of further investigations of the author of this article. These investigations (in terms of various representations of real numbers) include the generalized Salem functions and…
Since it first emerged in Wijsman's seminal work [29], the Wijsman topology has been intensively studied in the past 50 years. In particular, topological properties of Wijsman hyperspaces, relationships between the Wijsman topology and…
Author of this article created for the first time the method for finding solutions of the Minkowski problem for closed surfaces in Riemannian space.
The goal of this paper is to give a purely geometric proof of a theorem by Branko Gr\"unbaum concerning configuration of triangles coming from the classical Napoleon's theorem in planar Euclidean geometry.
Inscribability of polytopes is a classic subject but also a lively research area nowadays. We illustrate this with a selection of well-known results and recent developments on six particular topics related to inscribable polytopes. Along…
This is an update of my problem list.
In a series of papers and in his 2009 book on configurations Branko Gr\"unbaum described a sequence of operations to produce new $(n_{4})$ configurations from various input configurations. These operations were later called the "Gr\"unbaum…
This article provides a historical overview of Geometry of Numbers. 1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops, 6. Minkowski…
The emphasis in the developmet of theories with more than three spatial dimensions has recently shifted towards ``brane world'' picture, which assumes that ordinary matter (with possible exceptions of gravitons and other, hypothetic,…
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
Some achievements of the late Andrzej Kossakowski in the field of statistical physics and quantum theory are presented. We recall his attempt to find an analytical solution of the 3-dimensional Ising model and present a problem concerning…
\emph{Uncertain Graph} (also known as \emph{Probabilistic Graph}) is a generic model to represent many real\mbox{-}world networks from social to biological. In recent times analysis and mining of uncertain graphs have drawn significant…