Related papers: A brief introduction to Spectral Graph Theory
These are notes for a graduate-level introductory course on singularity categories.
A conjecture regarding the structure of expander graphs is discussed.
Spectral analysis connects graph structure to the eigenvalues and eigenvectors of associated matrices. Much of spectral graph theory descends directly from spectral geometry, the study of differentiable manifolds through the spectra of…
This article presents a very gentle introduction to the field of aperiodic order, aimed at a general audience. It is intended to provide a "Snapshot of Modern Mathematics" relating to the Oberwolfach mini-workshop "Dynamical versus…
These lecture notes provide an elementary introduction, within the framework of finite quantum systems, to recent developments in the theory of entropic fluctuations.
This paper serves as an introduction to the current book. It provides the basic notions of long-baseline optical/infrared interferome-try prior to reading all the subsequent chapters, and is not an extended introduction to the field.
Extremal Graph Theory is a very deep and wide area of modern combinatorics. It is very fast developing, and in this long but relatively short survey we select some of those results which either we feel very important in this field or which…
Signed graphs are graphs whose edges get a sign $+1$ or $-1$ (the signature). Signed graphs can be studied by means of graph matrices extended to signed graphs in a natural way. Recently, the spectra of signed graphs have attracted much…
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
Deep learning's success has been widely recognized in a variety of machine learning tasks, including image classification, audio recognition, and natural language processing. As an extension of deep learning beyond these domains, graph…
These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an introduction to neural networks for mathematics students at the…
A Short Course on Frame Theory.
This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college…
In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…
In this chapter we briefly review the basics of the theory of stellar evolution.
Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.
A brief introduction to the low-energy effective field theory of the standard model, chiral perturbation theory, is presented.
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…