Related papers: Notes on the Gabriel-Roiter measure

These notes are based on a series of five lectures given during the summer school ``Interactions between Homotopy Theory and Algebra'' held at the University of Chicago in 2004.

This is an expanded version of the lectures given at the Trieste Summer School 1992 on Low-dimensional Quantum Field Theories for Condensed Matter Physicists.

We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…

This is a survey on the subject of the title corresponding to three lectures I gave in June 2001 at the Workshop on Fourier Analysis and Convexity, at the Universita di Milano-Biccoca.

The article (Niebauer et al. 2011 Metrologia 48 154-163) reports on the important innovations enhancing the ability of absolute gravimeter to measure vertical gravity gradient along with the gravity acceleration. This comment suggests…

Chapters 1 to 4 are the lecture notes of my course "Real Algebraic Geometry I" from the winter term 2020/2021. Chapters 5 to 8 are the lecture notes of its continuation "Real Algebraic Geometry II" from the summer term 2021. Chapters 9 and…

In this paper we study higher Deligne--Lusztig representations of reductive groups over finite quotients of discrete valuation rings. At even levels, we show that these geometrically constructed representations coincide with certain induced…

These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author…

This work establishes a high-precision relativistic theoretical model: start from studying finite speed of light effect based on a coordinate transformation, and further extend the research methods to analyze the overall relativistic…

The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…

These are notes of a series of lectures on sieves, presented during the Special Activity in Analytic Number Theory, at the Max-Planck Institute for Mathematics in Bonn, during the period January--June 2002.

The aim of this note is to illustrate that the definition and construction of the Gabriel dimension for modular lattices in the classical sense is the same as the module case following H. Simmons.

This paper is a collection of lecture notes on modified gravity. Various modified gravity models formulated within the Riemannian formalism are discussed.

Examples of exact categories in representation theory are given by the category of Delta-filtered modules over quasi-hereditary algebras, but also by various categories related to matrix problems, such as poset representations or…

In these notes we focus on commutative finite-dimensional normed algebras and some basic examples.

These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.

To a finite group $G$, one can associate several notions of dimensions (or degrees). In this survey, we attempt to bring together some of the notions of dimensions or degrees defined using representations of the group in General Linear…

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…

The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…

This lecture notes are an expanded version of the course given at the ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa, September 30th - October 30th 2013. The lectures aim to explain the main steps of a new proof of…