Related papers: Monstrous Moonshine over Z?
We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.
I review our current understanding of superluminous supernovae, mysterious events 100 times brighter than conventional stellar explosions.
Milgrom's Modified Newtonian dynamics (MOND) provides an efficient way to summarize phenomenology of galaxies which does not lean on the notion of dark matter; it has great predictive power. Here I briefly review MOND as well as its…
We establish a result linking the Bouniakowsky conjecture and the density of polynomial roots to prime moduli.
Recent data indicate one or more moderately nearby supernovae in the early Pleistocene, with additional events likely in the Miocene. This has motivated more detailed computations, using new information about the nature of supernovae and…
Answering a question posed by Conway and Norton in their seminal 1979 paper on moonshine, we prove the existence of a graded infinite-dimensional module for the sporadic simple group of O'Nan, for which the McKay--Thompson series are weight…
We explore the real solutions to the Spherical Collapse Model in a non-flat Universe with a Cosmological Constant, and observe a possible situation for a fake or Ghost Collapse, in which an expanding overdense spherical region, turns around…
The anomaly for the Monster group $\mathbb{M}$ acting on its natural (aka moonshine) representation $V^\natural$ is a particular cohomology class $\omega^\natural \in \mathrm{H}^3(\mathbb{M},\mathrm{U}(1))$ that arises as a conformal field…
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.
Generalised moonshine is reviewed from the point of view of holomorphic orbifolds, putting special emphasis on the role of the third cohomology group H^3(G, U(1)) in characterising consistent constructions. These ideas are then applied to…
Scientific paper is devoted to establish connection of T-matrix - matrix of composite numbers 6h+1 v 6h-1 in special view - with Legendre's conjecture.
Since the discovery of the accelerated expansion of the Universe, the constraints on the equation of state $w_\text{DE}$ of dark energy, the stress-energy component responsible for the acceleration, have tightened significantly. These…
Astrophysical observations (usually explained by dark matter) suggest that classical mechanics could break down when the acceleration becomes extremely small (the approach known as modified Newtonian dynamics, or MOND). I present the first…
In this paper we give a proof of the Manickam-Mikl\'os-Singhi (MMS) conjecture for some partial geometries. Specifically, we give a condition on partial geometries which implies that the MMS conjecture holds. Further, several specific…
Dark energy and the accelerated expansion of the universe have been the direct predictions of the distant supernovae Ia observations which are also supported, indirectly, by the observations of the CMB anisotropies, gravitational lensing…
Under certain assumptions, we prove an anticyclotomic analogue of the "weak main conjecture" \`a la Mazur and Tate for modular forms over a large class of cyclic ring class extensions.
The orbital motion of inspiralling and coalescing black hole binaries can be investigated using a variety of approximation schemes and numerical methods within general relativity: post-Newtonian expansions, black hole perturbation theory,…
In 1997, an extension of general relativity was proposed that predicts the dark energy density \Lambda\ to vary linearly with the total number of macroscopic black holes in the universe. We explore this prediction and find that \Lambda\…
Geometric modularity has recently been conjectured to be a characteristic feature for flux vacua with $W=0$. This paper provides support for the conjecture by computing motivic modular forms in a direct way for several string…
Before 1998 the universe expansion was thought to be slowing down. After 1998 the universe expansion is thought to be accelerating up. This change of the belief is motivated by the observed brightness of the high redshift supernova Ia…