Related papers: Monstrous Moonshine over Z?
We propose a version of the volume conjecture that would relate a certain limit of the colored Jones polynomials of a knot to the volume function defined by a representation of the fundamental group of the knot complement to the special…
The cosmological standard model at present is widely accepted as containing mainly things we do not understand. In particular the appearance of a Cosmological Constant, or dark energy, is puzzling. This was first inferred from the Hubble…
This article explores the different formation scenarios of the Kronian moons system in the context of a highly dissipative Saturn, with the objective of identifying the most likely of these scenarios. First, we review the diversity of…
Nekrashevych conjectured that the iterated monodromy groups of quadratic polynomials with preperiodic critical orbit have intermediate growth. We illustrate some of the difficulties that arise in attacking this conjecture and prove…
We construct a model of moonshine phenomenon based on the use of N=2 superconformal algebra. We consider an extremal Jacobi form of weight 0 and index 2, and expand it in terms of N=2 massless and massive representations. We find the…
The Olbers conjecture, that under reasonable assumptions, light from the stars should sum at the Earth to make the sky bright at night, has been a subject of study since the early 19th century. It has been incorporated into some of modern…
The Weak Gravity Conjecture is a nontrivial conjecture about quantum gravity that makes sharp, falsifiable predictions which can be checked in a broad range of string theory examples. However, in the presence of massless scalar fields…
Cosmology, high-energy physics and astrophysics are converging on the study of large-scale magnetic fields. While the experimental evidence for the existence of large-scale magnetization in galaxies, clusters and superclusters is rather…
Strong cosmic censorship conjecture has been one of the most important leap of faith in the context of general relativity, providing assurance in the deterministic nature of the associated field equations. Though it holds well for…
In 2008, Haglund, Morse and Zabrocki formulated a Compositional form of the Shuffle Conjecture of Haglund et al. In very recent work, Gorsky and Negut by combining their discoveries with the work of Schiffmann-Vasserot on the symmetric…
Anomalous redshifts of some galactic objects such as binary stars, early-type stars in the solar neighborhood, and O stars in a star clusters are discussed. It is shown that all these phenomena have a common characteristic, that is, the…
We report determinations of the molybdenum abundances in five mildly to extremely metal-poor turnoff stars using five Mo II lines near 2000A. In two of the stars, the abundance of molybdenum is found to be extremely enhanced, as high or…
We provide a holographic dual description of Milgrom's scaling associated with galactic rotation curves. Our argument is based on the recent entropic reinterpretation of Newton's laws of motion. We propose a duality between cold dark matter…
We highlight recent theoretical and observational progress in several areas of neutron star astrophysics, and discuss the prospect for advances in the next decade.
We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
Weak lensing observations and supernova observations, combined with CMB observations, can both provide powerful constraints on dark energy properties. Considering statistical errors only, we find luminosity distances inferred from 2000…
A combination of ground-based and spacecraft observations has uncovered two black holes of 10 billion solar masses in the nearby Universe. The finding sheds light on how these cosmic monsters co-evolve with galaxies.
The codimension-three conjecture states that any regular holonomic module extends uniquely beyond an analytic subset with codimension equal to or larger than three. We give a proof of this conjecture.
Recently a conjecture has been proposed which attaches (mock) modular forms to the largest Mathieu group. This may be compared to monstrous moonshine, in which modular functions are attached to elements of the Monster group. One of the most…