Related papers: A Breakthrough in Sphere Packing: The Search for M…
One of the most spectacular scientific breakthroughs in past decades was using measurements of the fluctuations in the cosmic microwave background (CMB) to test precisely our understanding of the history and composition of the Universe.…
We explain in some detail the geometric structure of spheres in any dimension. Our approach may be helpful for other homogeneous spaces (with other signatures) such as the de Sitter and anti-de Sitter spaces. We apply the procedure to the…
The simplicity of hard spheres as a model system is deceptive. Although the particles interact solely through volume exclusion, that nevertheless suffices for a wealth of static and dynamical phenomena to emerge, making the model an…
Studies on experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects…
The recent progress in establishing the existence of finite neutrino masses and mixing between generations of neutrinos has been remarkable, if not astounding. The combined results from studies of atmospheric neutrinos, solar neutrinos, and…
The contact number of a packing of finitely many balls in Euclidean $d$-space is the number of touching pairs of balls in the packing. A prominent subfamily of sphere packings is formed by the so-called totally separable sphere packings:…
The following conjecture was proposed in 2010 by S. Lando. Let M and N be two unions of the same number of disjoint circles in a sphere. Then there exist two spheres in 3-space whose intersection is transversal and is a union of disjoint…
Given a sphere of any radius $r$ in an $n$-dimensional Euclidean space, we study the coverings of this sphere with solid spheres of radius one. Our goal is to design a covering of the lowest covering density, which defines the average…
We prove topological sphere theorems for RCD(n-1, n) spaces which generalize Colding's results and Petersen's result to the RCD setting. We also get an improved sphere theorem in the case of Einstein stratified spaces.
The main purpose of this article is to demonstrate three techniques for proving algebraicity statements about circle packings. We give proofs of three related theorems: (1) that every finite simple planar graph is the contact graph of a…
In this short note we provide a new proof of the recent result of Han and Nashimura on the separation of spherical convex sets established in arXiv:2002.06558. Our proof is based on a result stated in locally convex spaces.
We present the first systematic algorithm to estimate the maximum packing density of spheres when the grain sizes are drawn from an arbitrary size distribution. With an Apollonian filling rule, we implement our technique for disks in 2d and…
We derive a singular version of the Sphere Covering Inequality which was recently introduced in [42], suitable for treating singular Liouville-type problems with superharmonic weights. As an application we deduce new uniqueness results for…
In this article we obtain linear programming bounds for the maximal sphere packing density of commutative spaces. A special case of our results solves a conjecture by Cohn and Zhao on linear programming bounds for sphere packings in…
The field of neutrino physics is currently very exciting, with several recent results pointing to new physics. I will give an overview of the current experimental situation, focusing primarily on neutrino oscillation results. The data are…
Recent observations by H.E.S.S. and MAGIC strongly suggest that the Universe is more transparent to very-high-energy gamma rays than previously thought. We show that this fact can be reconciled with standard blazar emission models provided…
The purpose of these notes is describe the state of progress on the restriction problem in harmonic analysis, with an emphasis on the developments of the past decade or so on the Euclidean space version of these problems for spheres and…
In this talk I give an introduction and present some recent progress towards understanding the cohomology rings of character varieties of Riemann surfaces, such as the proof of the $P=W$ conjecture and the computation of the…
The magic "Harry Potter's cloak" has been the dream of human beings for really long time. Recently, transformation optics inspired from the advent of metamaterials offers great versatility for manipulating wave propagation at will to create…
Multi-messenger astrophysics, a long-anticipated extension to traditional and multiwavelength astronomy, has recently emerged as a distinct discipline providing unique and valuable insights into the properties and processes of the physical…