Related papers: On the basic structure theorems of global singular…
This is an exposition of some basic ideas in the realm of Global Inverse Function theorems. We address ourselves mainly to readers who are interested in the applications to Differential Equations. But we do not deal with those applications…
We summarize the main ideas of General Relativity and Lorentzian geometry, leading to a proof of the simplest of the celebrated Hawking-Penrose singularity theorems. The reader is assumed to be familiar with Riemannian geometry and point…
This brief set of notes presents a modest introduction to the basic features entering the construction of supersymmetric quantum field theories in four-dimensional Minkowski spacetime, building a bridge from similar lectures presented at a…
We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories,…
This paper presents a generalized version of a theorem of Grzegorek and Labuda in category bases and also endeavours to establish a variant formulation of the same in Marczewski structures.
We give simple characterizations of contact 1-forms in terms of Dirac structures. We also relate normal almost contact structures to the theory of Dirac structures.
In the present work, we introduce the notion of a hyper-atom and prove their main structure theorem. We then apply the global isoperimetric methodology to give a new proof for Kemperman's structure Theory and a slight improvement.
We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities…
We give down-to-earth proofs of the structure theorems for persistence modules.
This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…
Cell structures were introduced by W. Debski and E. Tymchatyn as a way to study some classes of topological spaces and their continuous functions by means of discrete approximations. In this work we weaken the notion of cell structure and…
This paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structure is a topological invariant that is characterized by the…
A majority of established quantum generalizations of discrete structures are shown to be instances of a single quantum generalization. In particular, the quantum graphs of Duan, Severini and Winter, the quantum metric spaces of Kuperberg…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
These lectures present some basic facts in field theory necessary to understand the quantum theory of the Standard Model of weak and electromagnetic interactions.
The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.
We deal with the existence of universal members in a given cardinality for several classes. First we deal with classes of Abelian groups, specifically with the existence of universal members in cardinalities which are strong limit singular…
A rough overview is given over the most essential structures underlying all working quantum theoretical models as well as axiomatic and algebraic quantum field theory .
Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ with the same…