Related papers: An Introduction To Small Divisors
This is a survey of the language of polyhedral divisors describing T-varieties. This language is explained in parallel to the well established theory of toric varieties. In addition to basic constructions, subjects touched on include…
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information…
A new approach to disintegration of measures is presented, allowing one to drop the usually taken separability assumption. The main tool is a result on fibers in the spectrum of algebra of essentially bounded functions established recently…
This Master's thesis presents a study of the basic properties of the s-fractional perimeter and of the regularity theory of the corresponding s-minimal sets. In particular, we give full detailed proofs for all the Theorems contained in the…
This book is divided into two parts. In the first part we give an elementary introduction to computational physics consisting of 21 simulations which originated from a formal course of lectures and laboratory simulations delivered since…
We review various derivations of the partition function of the two-dimensional Ising Model of ferromagnetism and proofs of the stability of matter, paying attention to passages where there would appear to be a lacuna between steps or where…
This thesis is divided into three parts. In the first part, we give an introduction to J. Harrison's theory of differential chains. In the second part, we apply these tools to generalize the Cauchy theorems in complex analysis. Instead of…
We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
We develop sheaf theory in the context of difference algebraic geometry. We introduce categories of difference sheaves and develop the appropriate cohomology theories. As specializations, we get difference Galois cohomology, difference…
We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian perturbations of the dispersive Degasperis-Procesi equation on the circle. The overall strategy in KAM theory for quasi-linear PDEs is based on Nash-Moser…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
The Gromoll-Meyer's generalized Morse lemma (so called splitting lemma) near degenerate critical points on Hilbert spaces, which is one of key results in infinite dimensional Morse theory, is usually stated for at least $C^2$-smooth…
Contents 1 Mappings and distortion 2 The mathematics of good behavior much of the time, and the BMO frame of mind 3 Finite polyhedra and combinatorial parameterization problems 4 Quantitative topology, and calculus on singular spaces 5…
The study of cosmological correlators, and more generally Feynman integrals, is greatly aided by considering them as solutions to differential equations. Often, such systems of differential equations are reducible, which, broadly speaking,…
The Abel Jacobi theorem is an important result of algebraic geometry. The theory of divisors and the Riemann bilinear relations are fundamental to the developement of this result: if a point O is fixed in a Riemann compact surface X of…
The aim of this paper is to provide another perspective on secant varieties on algebraic curves by reformulating the problem in terms of refined de Jonqui\`eres divisors, that is divisors on the curve with prescribed multiplicities and…
In this article, we compile the work done by various mathematicians on the topic of the fixed divisor of a polynomial. This article explains most of the results concisely and is intended to be an exhaustive survey. We present the results on…
An elementary introduction to functional methods and the Schwinger-Dyson equations is presented. Emphasis is placed on practical topics not normally covered in textbooks, such as a diagrammatic method for generating equations at high order,…
This work looks at the theory of octonionic slice regular functions through the lens of differential topology. It proves a full-fledged version of the Open Mapping Theorem for octonionic slice regular functions. Moreover, it opens the path…