Related papers: GR 15 Proceedings A5(ii) Computer Methods in GR: A…
Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It allows for the computation of several cohomological invariants of an algebraic variety. In particular, its application to enumerative algebraic geometry led to…
The last two decades have seen a major expansion in the availability, size, and precision of time-domain datasets in astronomy. Owing to their unique combination of flexibility, mathematical simplicity and comparative robustness, Gaussian…
This work presents instructive, yet comprehensive derivation of quantized gravity theories in relativistic, classical, and semi-classical spacetime structure based on the Poincar\'e, Galilean, and Bargmann algebra, respectively. The…
We present a generic C++ design to perform efficient and exact geometric computations using lazy evaluations. Exact geometric computations are critical for the robustness of geometric algorithms. Their efficiency is also critical for most…
We describe recent attempts at discretizing canonical quantum gravity in four dimensions in terms of a connection formulation. This includes a general introduction, a comparison between the real and complex connection approach, and a…
We consider the domain of applicability of general relativity (GR), as a classical theory of gravity, by considering its applications to a variety of settings of physical interest as well as its relationship with real observations. We argue…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
This posting announces public availability of the GALAXY software package developed by the author over the past 40 years. It is a highly efficient code for the evolution of (almost) isolated, collisionless stellar systems, both disk-like…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
The numerical relativity session at GR18 was dominated by physics results on binary black hole mergers. Several groups can now simulate these from a time when the post-Newtonian equations of motion are still applicable, through several…
This essay aims at emphasizing the potential of a synergy between quantum gravity and the quantum computing technologies. Such a combination would be beneficial for both understanding the Planck scale physics and the stimulation of…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
I briefly discuss some attempts to construct a consistent modification to General Relativity (GR) that might explain the observed late-time acceleration of the universe and provide an alternative to dark energy. I mention the issues facing…
Studies of issues related to computability and computational complexity involve the use of a model of computation. Pivotal to such a model are the computational processes considered. Processes of this kind can be described using an…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
Quantum computer programming is emerging as a new subject domain from multidisciplinary research in quantum computing, computer science, mathematics (especially quantum logic, lambda calculi, and linear logic), and engineering attempts to…
These are expanded lecture notes of a series of expository talks surveying basic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomology. You…
In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has…
In (S.B. Ekhad and D. Zeilberger, 2020) an exciting case study has been initiated in which experimental mathematics and symbolic computation are utilized to discover new properties concerning the so-called Absent-Minded Passengers Problem.…