Related papers: M\"obius strips before M\"obius: Topological hints…
It has long been known that strings wound around incontractible cycles can play a vital role in cosmology. In particular, in a spacetime with toroidal spatial hypersurfaces, the dynamics of the winding modes may help yield three large…
This is an expository and introductory note on some results obtained in "Coisotropic embeddings in Poisson manifolds" (ArXiv math/0611480). Some original material is contained in the last two sections, where we consider linear Poisson…
The influence of the topology and curvature of objects on photonic properties represents an intriguing fundamental problem from cosmology to nanostructure physics. The classical topological transition from a ring to a M\"obius strip is…
An arbitrary Feynman graph for string field theory interactions is analysed and the homeomorphism type of the corresponding world sheet surface is completely determined even in the non-orientable cases. Algorithms are found to mechanically…
The topology of the observable Universe is not yet known. The most significant observational sign of a non-trivial topology would be multiple images (``ghosts'') of a single object at (in general) different sky positions and redshifts. It…
In 1966, David Mumford created a drawing of $\operatorname{Proj} \mathbb Z [X,Y]$ in his book, "Lectures on Curves on an Algebraic Surface". In following, he created a photo of a so-called 'arithmetic surface' $\operatorname{Spec} \mathbb Z…
We establish the analogue for maps on trees of the result established in two papers by the first author for interval maps, that a continuous self- map for which all but countably many points have at least m preimages (and none have less…
Multiple gaps in the tight-binding band of a pentagonal lattice are found. Unlike the Cairo pentagonal lattice this lattice is made of irregular pentagons with arms of different lengths. The tight-binding Hamiltonian is exactly solved to…
An antimagic labeling of a directed graph $D$ with $m$ arcs is a bijection from the set of arcs of $D$ to $\{1,\dots,m\}$ such that all oriented vertex sums of vertices in $D$ are pairwise distinct, where the oriented vertex sum of a vertex…
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…
We study the topology of several music recommendation networks, which rise from relationships between artist, co-occurrence of songs in playlists or experts' recommendation. The analysis uncovers the emergence of complex network phenomena…
We review our knowledge of the mixing properties of magnetic OB stars and discuss whether the observational data presently available support, as predicted by some theoretical models, the idea that magnetic phenomena favour the transport of…
This article reviews recent work with M.R.Douglas and B. Shiffman on statistics of vacua in type IIb flux compactions of string/M theory.
An old problem raised independently by Jacobson and Sch\"onheim asks to determine the maximum $s$ for which every graph with $m$ edges contains a pair of edge-disjoint isomorphic subgraphs with $s$ edges. In this paper we determine this…
The topic of this treatise is a combinatorial technique called Graph Pebbling. We investigate pebbling numbers, weight functions, flow networks, hypercubes, and the zero-sum conjecture of Erd\H{o}s and Lemke. This investigation is a…
The bisection of trapezoids by transversal lines has many examples in Babylonian mathematics. In this article, we study a similar problem in Elamite mathematics, inscribed on a clay tablet held in the collection of the Louvre Museum and…
A result of Allock [1](arXiv:math/9907194) states that certain orbifold braid groups contain Artin groups of type $D_n$, $\tilde{B}_n$ and $\tilde{D}_n$ as finite index subgroups. The underlying orbifolds have at most two cone points of…
Aims: Our aim is to provide an observational view of the old Disc structure of the Milky Way galaxy using the distribution of red clump stars. The spiral arms, warp structure, and other asymmetries present in the Disc are re-visited using a…
Symbiotic binaries are putative progenitors of type Ia supernovae. The census of Galactic symbiotic binaries is so incomplete that we cannot reliably estimate the total population of these stars, and use it to check whether that number is…
We describe an infinite family of edge-decompositions of complete graphs into two graphs, each of which triangulate the same orientable surface. Previously, such decompositions had only been known for only a few complete graphs. These…