Related papers: 13 or 14, Halloween surprise
This article intends to provide an introduction to the construction of small exotic 4-manifolds. Some of the necessary background is covered. An exposition is given of J. Park's construction in arXiv:math.GT/0311395 of an exotic…
There is a relationship between the Borromean rings, the icosahedron and something called the Poincar\'e homology sphere. This relationship is explored in a wandering path that introduces fundamental ideas from topology and a geometric…
I present a jaunty little $[[14, 3, 3]]$ non-CSS surface code that can be described using a rhombic dodecahedron. Do with it what you will.
Motivated by the discovery of hidden-charm strange pentaquarks, we conduct a systematic study of the magnetic moments of the hidden-bottom strange pentaquarks in molecular picture. We calculate magnetic moments of hidden-bottom strange…
These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…
A particular discrete rhombohedral lattice consisting of four symmetrically interlaced cuboctahedral point lattices is described that is interesting because of the high degree of symmetry it exhibits. The four constituent cuboctahedral…
We introduce Quintessence: a family of burr puzzles based on the geometry and combinatorics of the 120-cell. We discuss the regular polytopes, their symmetries, the dodecahedron as an important special case, the three-sphere, and the…
The purpose of these lecture notes is to give a quick and introductory overview of holographic superconductors. Besides the actual description of the standard holographic superconductor, attention is paid to the motivations and the relation…
This paper will be splited into two papers and submited later.
There are two hypotheses on Leonardo's polyhedron based on the Pseudo-RCO and drawn for Luca Pacioli's book: Leonardo made an error, or: Leonardo draw it with intention, as it is. We give arguments, which support the Intention-hypothesis.
We find that the model of a black hole plus an exterior halo of quadrupoles and octopoles recently proposed by us is more chaotic than previously detected. In fact, the quadrupolar component gives rise also to a chaotic behavior, found…
We investigate on exotic tetraquark hadrons of the kind [cs][cbar sbar] by computing their spectrum and decay modes within a constituent diquark-antidiquark model. We also compare these predictions with the present experimental knowledge.
This paper presents an additional class of regular polyhedra--envelope polyhedra--made of regular polygons, where the arrangement of polygons (creating a single surface) around each vertex is identical; but dihedral angles between faces…
The space of $4 \times 4$ special orthogonal matrices with zeros on the diagonal decomposes into the union of $14$ irreducible surfaces whose intersections are beautifully encoded by the cuboctahedron. Using this decomposition, we exhibit a…
A conjecture regarding the structure of expander graphs is discussed.
We start with an ``algebraic'' RSK-correspondence due to Noumi and Yamada. Given a matrix $X$, we consider a pyramidal array of solid minors of $X$. It turns out that this array satisfies an algebraic variant of octahedron recurrence. The…
A brief review of the history of the discovery of the deuteron in provided. The current status of both experiment and theory for the elastic electron scattering is then presented.
See hep-th/9903228.
With the negative sign for $\sqrt m_s$, the quarks strange, charm and bottom make a Koide tuple. It continues the c-b-t tuple previously found by Rodejohann and Zhang and, more peculiar, it is quasi-orthogonal to the original lepton…
Two types of Poisson pencils connected to classical R-matrices and their quantum counterparts are considered. A representation theory of the quantum algebras related to some symmetric orbits in $sl(n)^*$ is constructed. A twisted version of…