ABSTRACT: The purpose of this short but difficult paper is to revisit the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT) in the light of a modern approach to nonlinear ...

ABSTRACT: The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential ...

In this project, we attempt to reformulate various notions from classical commutative algebra (such as flatness, regularity, smoothness, etc.) in an entirely categorical manner, so as to be able to ...

A Macaulay2 package to deal with t-spread ideals of a polynomial ring. Some details can be found in this paper.

Ordinary commutative algebraic geometry is based on commutative polynomial algebras over an algebraically closed field k. Here we make a natural generalization to matrix polynomial k-algebras which ...