Related papers: Horizons Inside Classical Lumps
New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems…
These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.
The category of compact Hausdorff spaces is the base of tripos. As such it can be freely completed to an elementary topos.
This short note is some obvious mathematical addendum to our papers on Wilson loops on polygon-like contours with circular edges \cite{Dorn:2020meb,Dorn:2020vzj}. Using the technique of osculating spheres and circles we identify the…
Black holes in general relativity are characterized by their trapping horizon, a one-way membrane that can be crossed only inwards. The existence of trapping horizons in astrophysical black holes can be tested observationally using a…
We prove that in many cases the existence of an extremal metric for some Laplace eigenvalue in a conformal class allows to find extremal metrics in conformal classes close by. As a consequence and as part of the arguments we obtain…
We review various combinatorial problems with underlying classical or quantum integrable structures. (Plenary talk given at the International Congress of Mathematical Physics, Aalborg, Denmark, August 10, 2012.)
We investigate analytically a large-scale coherence in the orientation of galaxies embedded in two-dimensional sheet-like structures in the frame of the tidal torque theory. Assuming that the galaxy spin and the surrounding matter fields…
We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen…
We present ongoing work on Guppy, a domain-specific language embedded in Python that allows users to write high-level hybrid quantum programs with complex control flow in Pythonic syntax, aiming to run them on actual quantum hardware.
We improve the previuosly known bound for some vertex Folkman numbers.
This is an example on the cohomology of threefolds.
Tangles of loops which approximate an aspect of the Kerr-Newman black hole metrics at large scales compared to the Planck length are constructed. The physical aspect the tangles approximate is discussed. This construction may be useful in…
For a much better-founded theory, check Wing Ip, GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L16203, doi:10.1029/2005GL025386, 2006 (see also http://www.agu.org/journals/gl/gl0616/2005GL025386/)
We suggest a construction of virtual fundamental classes of certain types of moduli spaces.
A hybrid methodology for the resolution of text-level ellipsis is presented in this paper. It incorporates conceptual proximity criteria applied to ontologically well-engineered domain knowledge bases and an approach to centering based on…
From the microscopic point of view, realistic black holes are time-dependent and the teleological concept of event horizon fails. At present, the apparent or the trapping horizon seem its best replacements in various areas of black hole…
We discuss the method of bounding suprema of canonical processes based on the inclusion of their index set into a convex hull of a well-controlled set of points. While the upper bound is immediate, the reverse estimate was established to…
This is a chapter surveying the current state of our understanding of tilings with infinite local complexity. It is intended to appear in the volume {\em Directions in Aperiodic Order}, D. Lenz, J. Kellendonk, and J. Savienen, eds.
We review the different proposals and attempts to identify the ``horizon molecules" that would give a kinematical estimation for the black hole entropy in causal set theory. The proposals are presented according to their chronological…