Related papers: Geometrical joke(r?)s for SETI
In a recent preprint, we discussed geometric lifts, and in particular the notion of St\"ackel lift. In this note, we wish to clarify several aspects raised in the comment arXiv:2511.05765.
We give a brief survey of some of the geometry of mirror symmetry, written in 2004 for the "Encyclopaedia of Mathematical Physics". Probably a little bit out of date now in a few places, but hey.
We survey results concerning sharp estimates on volumes of sections and projections of certain convex bodies, mainly $\ell_p$ balls, by and onto lower dimensional subspaces. This subject emerged from geometry of numbers several decades ago…
I review the scientific and technical history of the Search for Extraterrestrial Intelligence (SETI), discuss the impact of the political involvement, and speculate on the nature of a successful detection and its potential social and…
Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.
The determination of the geodesics in Scharzschild black hole and de Sitter space.
The correspondence between black holes and colliding waves extends to cover the near horizon geometry of rotating black holes and colliding waves with cross polarization. Extreme Kerr and Kerr-Newman geometries are given as examples.
General results on equatorial geodesics are exposed in the case of circular spacetimes featuring an equatorial reflection symmetry. The way the geodesic equation equivalently rewrites in terms of an effective potential is explicitly…
In this short note we establish new refinements of multidimensional Szemeredi and polynomial van der Waerden theorems along the shifted primes.
Numerical Relativity has been using orbifolds for a long time, although they appear under different names in the literature. We review orbifolds previously used in simulations also discuss some that have not been used yet but are likely to…
Our recent results concerning the transformation under isometries of the conserved quantities on de Sitter manifolds, allow us to define the rest frame and study the relative geodesic motion in terms of conserved momentum, revealing thus…
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
We reveal a general explicit relation between the statistics of delay times in one-channel reflection from a mesoscopic sample of any spatial dimension and the statistics of the eigenfunction intensities in its closed counterpart. This…
The relative geodesic motion in central charts (i.e. static and spherically symmetric) on the $(1+3)$-dimensional de Sitter spacetimes is studied in terms of conserved quantities. The Lorentzian isometries are derived, relating the…
Several physical systems (two identical particles in two dimensions, isotropic oscillator and Kepler system in a 2-dim curved space) and mathematical structures (quadratic algebra QH(3), finite W algebra $\bar {\rm W}_0$) are shown to…
A definition of space-time metric deformations on an $n$-dimensional manifold is given. We show that such deformations can be regarded as extended conformal transformations. In particular, their features can be related to the perturbation…
This paper is a short historical note about the origin of the Pole-Barn and the Fat Man Paradoxes
We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schrödinger and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize…
We investigate a sequence of quadratic topological terms of the Chern-Simons type in different spacetime dimensions, related by dimensional compactification and sharing the properties of topological mass generation and statistical…
Some problems related to the structure of higher terms of the epsilon-expansion of Feynman diagrams are discussed.