Related papers: On the use of algebraic programming in the general…
We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded…
In this manuscript we review the theoretical foundations of gravitational waves in the framework of Albert Einstein's theory of general relativity. Following Einstein's early efforts we first derive the linearised Einstein field equations…
The confrontation between Einstein's theory of gravitation and experiment is summarized. Although all current experimental data are compatible with general relativity, the importance of pursuing the quest for possible deviations from…
On the occasion of the 50th anniversary since the beginning of the search for gravitational waves at the Max Planck Society, and in coincidence with the 25th anniversary of the foundation of the Albert Einstein Institute, we explore the…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
The idea that the Universe is a program in a giant quantum computer is both fascinating and suffers from various problems. Nonetheless, it can provide a unified picture of physics and this can be very useful for the problem of Quantum…
In the era of gravitational-wave astronomy, general-relativistic simulations of compact objects play a role of paramount importance. These calculations can be performed with the Einstein Toolkit, an open-source and community-supported…
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
A survey of algebraic approaches to various problems in nuclear physics is given. Examples are chosen from pairing of many-nucleon systems, nuclear structure, fusion reactions below the Coulomb barrier, and supernova neutrino physics to…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
This is a substantially expanded version of a chapter-contribution to "The Springer Handbook of Spacetime", edited by Abhay Ashtekar and Vesselin Petkov, published by Springer Verlag in 2014. This contribution introduces the reader to the…
We compare Einstein-Boltzmann solvers that include modifications to General Relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily…
Einstein algebra, the concept due to Geroch, is essentially general relativity in an algebraic disguise. We introduce the concept of Einstein-Grassmann algebra as a superalgebra (defining a supermanifold) which is also an Einstein algebra.…
The aim of this work is to develop a study from the perspective of Abstract Algebraic Logic of some bilattice-based logical systems introduced in the nineties by Ofer Arieli and Arnon Avron. The motivation for such an investigation has two…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
We outline a program in the area of formalization of mathematics to automate theorem proving in algebra and algebraic geometry. We propose a construction of a dictionary between automated theorem provers and (La)TeX exploiting syntactic…
We consider some of the epistemic benefits of exploring "theory space" in the context of modifications of general relativity with intended applications in cosmology. We show how studying modifications of general relativity can help in…
Based on the distinction between the covariant and contravariant metric tensor components in the framework of the affine geometry approach and the s.c. "gravitational theories with covariant and contravariant connection and metrics", it is…
We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…
These are notes of a series of lectures on sieves, presented during the Special Activity in Analytic Number Theory, at the Max-Planck Institute for Mathematics in Bonn, during the period January--June 2002.