Related papers: A Short Course on Frame Theory

This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.

We develop a fundamental framework for and extend the theory of rough paths to Lipschitz-gamma manifolds.

This paper develops the basic theory of formal schemes over fields in the supersymmetric setting. We introduce the notion of a formal superscheme and investigate some of its fundamental properties. Particular emphasis is placed on the study…

We initiate the computability-theoretic study of ringed spaces and schemes. In particular, we show that any Turing degree may occur as the least degree of an isomorphic copy of a structure of these kinds. We also show that these structures…

In this short survey we report on the theory of biharmonic maps between Riemannian manifolds.

These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.

Fracterms are introduced as a proxy for fractions. A precise definition of fracterms is formulated and on that basis reasonably precise definitions of various classes of fracterms are given. In the context of the meadow of rational numbers…

The talk contains a brief introduction string theory, followed by a discussion of some of the recent developments.

Elementary review article on quantum cryptography.

This monograph is on convex real projective structures on strongly tame n-orbifolds with some appropriate conditions on ends.

ICM lecture on minimal models and moduli of varieties.

We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools from analytic number theory.

The aim of this paper is to provide a largely self-contained, compact and comprehensible introduction to the basic ideas behind correlation geometry, which underlies the theory of causal fermion system (CFS). A key focus here is on the…

The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…

Motivated by issues in string theory and M-theory, we provide a pedestrian introduction to automorphic forms and theta series, emphasizing examples rather than generality.

Instantaneous derivation of the Thomas precession with only basic vector calculus.

We consider the problem of rescaling the lengths of a finite frame thereby transforming it into a tight one. Such frames are called scalable and have received a lot of attention in recent years. In this note we investigate the question in…

This is an introduction to some of the most probabilistic aspects of free probability theory.

This paper investigates scalable frame in ${\mathbb R}^n$. We define the reduced diagram matrix of a frame and use it to classify scalability of the frame under some conditions. We give a new approach to the scaling problem by breaking the…

This short note is an "elementary'' introduction to the conjectural theory of motives.