Related papers: Branko Gr\"unbaum in many dimensions
This article presents the construction of finitely generated branch groups with uncountably many maximal subgroups using embedding techniques. This addresses a question posed by Grigorchuk.
This paper collects into one place (most of) my answers to the questions Maximilian Schlosshauer posed in his interview volume, "Elegance and Enigma: The Quantum Interviews" (Springer, Frontiers Collection, 2011).
After reviewing how M-theory subsumes string theory, I report on some new and interesting developments, focusing on the ``brane-world'': circumventing no-go theorems for supersymmetric brane-worlds, complementarity of the Maldacena and…
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
Expository article on the problem of determining the maximum number of equiangular lines with a fixed angle, and the associated problem of second eigenvalue multiplicity in graphs.
We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly different properties to the previous approaches of Colman-Grant,…
We provide a list of (mainly unsolved) problems in ordered and orderable groups. These were originally compiled 10 years ago by the last two authors. New problems have been added to the list. Progress on some of these is noted and…
This document is an exposition of an assortment of open problems arising from the exact enumeration of (perfect) matchings of finite graphs. Roughly half have been solved at the time of this writing; see the document "Twenty Open Problems…
We present five open problems in quantum gravity which one might reasonably hope to solve in the next decade. Hints appearing in the literature are summarized for each one.
Growing non-singular solution of 6-dimensional Einstein equations for the 4-brane in infinite transversal 2-space is found. This solution provides gravitational trapping of matter and 4-dimensional gravity on the brane without extra…
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
The aim of this contribution is to provide a short introduction to recently investigated models in which our accessible universe is a four-dimensional submanifold, or brane, embedded in a higher dimensional spacetime and ordinary matter is…
The aim of this paper is the determination of the largest $n$-dimensional polytope with $n+3$ vertices of unit diameter. This is a special case of a more general problem proposed by Graham.
I construct solutions to Einstein's equations in 6 dimensions with bulk cosmological constant and intersecting 4-branes. Solutions exist for a continuous range of 4-brane tension, with long distance gravity localized to a 3+1 dimensional…
In this small paper we bring together various open problems on geometric multidimensional continued fractions.
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
Hyperfiniteness or amenability of measurable equivalence relations and group actions has been studied for almost fifty years. Recently, unexpected applications of hyperfiniteness were found in computer science in the context of testability…
This article is a snap-shot of a web site, which has been collecting open problems in quantum information for several years, and documenting the progress made on these problems. By posting it we make the complete collection available in one…
In this survey, we review the many faces of the Hornich-Hlawka inequality. Several open problems that seem of utmost interest are mentioned.
These notes give an introductory review on brane cosmology. This subject deals with the cosmological behaviour of a brane-universe, i.e. a three-dimensional space, where ordinary matter is confined, embedded in a higher dimensional…