Related papers: Spectral sequences via examples
These notes correspond rather accurately to the translation of the lectures given at the Fifth Mexican School of Particles and Fields, held in Guanajuato, Gto., in December~1992. They constitute a brief and elementary introduction to…
These are notes from my lecture at 4ECM in Stockholm (June 2004).
This is a collection of notes based on lectures given at IIT Madras in September 2019 and at IFT Madrid in November 2019. It is supposed to be a concise (and therefore not comprehensive) and pragmatic course on applied holography and…
The aim of this note is to prove that the set of proper normal subgroups of a group endowed with coarse lower topology is a spectral space.
These are lecture notes from a course given at the summer school "Heat kernels and spectral geometry: from manifolds to graphs" in Bregenz, Austria, 2022. They are designed to be accessible to doctoral level students, and include background…
We present a spectral sequence connecting the continuous and 'locally continuous' group cohomologies for topological groups. As an application it is shown that for contractible topological groups these cohomology concepts coincide. Similar…
These notes arose from three lectures on fusion system I gave at the University of Valencia in February 2023. We first consider fusion phenomena in classical group theory. Then we develop the abstract theory of fusion systems. Finally…
The paper consists of lecture notes for a mini-course given by the authors at the G\"okova Geometry \& Topology conference in May 2014. We start the exposition with tropical curves in the plane and their applications to problems in…
These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts. In particular, this includes a discussion of simplification…
These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.
We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.
These lectures are based on material which was presented in the 2025 Summer school at Funda\c{c}\~ao Getulio Vargas. The aim of this series is to introduce graduate students with a little background in the field of dynamical systems and…
These lecture notes where presented as a course of the CIMPA summer school in Manila, July 20-30, 2009, Semidefinite programming in algebraic combinatorics. This version is an update June 2010.
These lecture notes are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations: the Vinogradov C-spectral sequence and the C-cohomology, including the formulation in…
In these self-contained low prerequisite introductory notes we first present (in part 1) basic concepts of set theory and algebra without explicit category theory. We then present (in part 2) basic category theory involving a somewhat…
We give a very brief introduction to the machinery of spectral sequences, including the spectral sequence of a bicomplex. We then briefly introduce a generalisation of the spectral sequences of a bicomplex to the spectral sequences of…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
Motivated by representation theory we exhibit an interior structure to Catalan sequences and many generalisations thereof. Certain of these coincide with well known (but heretofore isolated) structures. The remainder are new.
These notes combine material from short lecture courses given in Paris, France, in July 2001 and in Srni, the Czech Republic, in January 2003. They discuss groups of symplectomorphisms of closed symplectic manifolds (M,\om) from various…