Related papers: Lectures on singularity categories
The purpose of these notes is to give a categorical presentation/analysis of homotopy type theory. The notes are incomplete as they stand (October 2017). The chapter on univalent tribes is missing. The references are not always connected to…
This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and…
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from…
These lecture notes are intended to cover some introductory topics in stochastic simulation for scientific computing courses offered by the IT department at Uppsala University, as taught by the author. Basic concepts in probability theory…
These are the lecture notes from my course in the January 2011 School on Moduli Spaces at the Newton Institute. I give an introduction to Higgs bundles and their application to the study of character varieties for surface group…
The aim of these lectures is to provide (experimental particle physics Ph.D.) students with an introduction to some of the core concepts and methods of QCD that are relevant in an LHC context.
We give an informal introduction to model categories, and treat three important examples in some details: the category of small categories, the category of dg algebras, and the category of small dg categories.
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
This lecture notes cover a Part III (first year graduate) course that was given at Cambridge University over several years on pseudo-differential operators. The calculus on manifolds is developed and applied to prove propagation of…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
As the title indicates
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…
Given a recollement of three proper dg algebras over a noetherian commutative ring, e.g. three algebras which are finitely generated over the base ring, which extends one step downwards, it is shown that there is a short exact sequence of…
These short lecture notes provide an introduction to some basic notions of F-theory with some special emphasis on its relation to Type IIB orientifolds with O7/O3-planes.
In this note we discuss Morita equivalence classes of arbitrary finitely presented algebras
These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…
Lecture notes delivered in Barcellona in the fall of 2003
We introduce and study the concept of cyclicity degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An…
The notes contain a streamlined account on stability of univariate polynomials and related problems
An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…