Related papers: M\"obius strips before M\"obius: Topological hints…
M\"obius inversion, originally a tool in number theory, was generalized to posets for use in group theory and combinatorics. It was later generalized to categories in two different ways, both of which are useful. We provide a unifying…
String graphs, that is, intersection graphs of curves in the plane, have been studied since the 1960s. We provide an expository presentation of several results, including very recent ones: some string graphs require an exponential number of…
In the first part of this paper I give an elementary overview about some number sequences which count various sorts of lattice paths in strips along the x-axis and compute their generating functions in terms of Fibonacci and Lucas…
This paper presents a construction of a folded paper ribbon knot that provides a constant upper bound on the infimal aspect ratio for paper M\"obius bands and annuli with arbitrarily many half-twists. In particular, the construction shows…
The recently discovered, ring-like structure just outside the Galactic disk in Monoceros is detected and traced among 2MASS M giant stars. We have developed a method to recover the signature of this structure from the distance probability…
Gordon and Litherland showed that all compact, unoriented, possibly non-orientable surfaces in $S^3$ bounded by a link are realted by attaching/deleting tubes and half twisted bands. In this note we give an elementary proof for this result.
Large-scale spiral arms have been revealed in scattered light images of a few protoplanetary disks. Theoretical models suggest that such arms may be driven by and co-rotate with giant planets, which has called for remarkable observational…
This is the written version of a short talk given at the University of Leipzig in December 1998. It reviews some general aspects of string theory from the viewpoint of the search for an unifying theory. Here, special emphasis lies on the…
Recently, there is an explosive growth of activities to understand stringy properties of orbifolds. In this article, we survey some of recent developments.
The study of the mathematics and geometry of ancient civilizations is a task which seems to be very difficult or even impossible to fulfil, if few written documents, or none at all, had survived from the past. However, besides the direct…
Using VLT/SPHERE near-infrared dual-band imaging and integral field spectroscopy we discovered an edge-on debris disk around the 17\,Myr old A-type member of the Scorpius-Centaurus OB association HD 110058. The edge-on disk can be traced to…
It is suggested that recent experiments provide evidence for modulations along the charged stripes in the striped phase of the cuprates. Furthermore, 1/8 doping is special because it is associated with a crossover: for lower doping the…
The different couplings of the dilaton to the U(1) gauge field of heterotic and Type I superstrings may leave an imprint on the relics of the very early cosmological evolution. Working in the context of the pre-big bang scenario, we discuss…
This note adds one diminimal map on the torus to the published set of 55. It also raises to 15 the number of vertices for which all diminimal maps on the torus are known.
The presence of magnetic fields at the surfaces of many massive stars has been suspected for decades, to explain the observed properties and activity of OB stars. However, very few genuine high-mass stars had been identified as magnetic…
Short, bijective proofs of identities for multisets of `hook pairs' (arm-leg pairs) of the cells of certain diagrams are given. These hook pair identities were originally found by Regev.
In arXiv:0910.1727 we find certain finite homomorphic images of Artin braid group into appropriate symmetric groups, which a posteriori are extensions of the symmetric group on n letters by an abelian group. The main theorem of this paper…
The amoebas associated to algebraic varieties are certain concave regions in the Euclidean space whose shape reminds biological amoebas. This term was formally introduced to Mathematics in 1994 by Gelfand, Kapranov and Zelevinski. Some…
A graph is closed when its vertices have a labeling by [n] with a certain property first discovered in the study of binomial edge ideals. In this article, we explore various aspects of closed graphs, including the number of closed labelings…
An overview of last seven years results concerning Sarnak's conjecture on M\"obius disjointness is presented, focusing on ergodic theory aspects of the conjecture.