What is a Module? (Abstract Algebra)
A module is a generalization of a vector space. You can think of it as a group of vectors with scalars from a ring instead of a field. In this lesson, we introduce the module, give a variety of examples, and talk about the ways in which modules and vector spaces are different from one an
From playlist Abstract Algebra
JavaScript Modules Past & Present
Modules provide structure to our code, grouping related data and functionality into reusable building blocks. However, prior to ES6, JavaScript did not have a built-in module system. This month's meetup will explore the history of modules through the advent of ES Modules, the first standar
From playlist Talks
Modular Forms | Modular Forms; Section 1 2
We define modular forms, and borrow an idea from representation theory to construct some examples. My Twitter: https://twitter.com/KristapsBalodi3 Fourier Theory (0:00) Definition of Modular Forms (8:02) In Search of Modularity (11:38) The Eisenstein Series (18:25)
From playlist Modular Forms
From playlist Programmieren mit Ruby mit Franz, Jan, Christiane
This lecture is part of an online course on rings and modules. We review basic properties of polynomials over a field, and show that polynomials in any number of variables over a field or the integers have unique factorization. For the other lectures in the course see https://www.youtu
From playlist Rings and modules
Notes by Keith Conrad to follow along: https://kconrad.math.uconn.edu/blurbs/linmultialg/modulesoverPID.pdf
From playlist Abstract Algebra 2
Commutative algebra 23 (Flat extensions)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we discuss flat extensions of rings. In particular we show that for flat extensions the homomorphisms of fini
From playlist Commutative algebra
0:00 Motivation for studying modules 4:45 Definition of a vector space over a field 9:31 Definition of a module over a ring 12:12 Motivating example: structure of abelian groups 16:05 Motivating example: Jordan normal form 19:44 What unifies both examples (spoiler): Structure theorem for f
From playlist Abstract Algebra 2
Commutative algebra 38 Survey of module properties
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give a short survey of some of the properties of modules, in particular free, stably free, Zariski locally free, projectiv
From playlist Commutative algebra
Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum), Lecture 5
Quiver moduli spaces are algebraic varieties encoding the continuous parameters of linear algebra type classification problems. In recent years their topological and geometric properties have been explored, and applications to, among others, Donaldson-Thomas and Gromov-Witten theory have
From playlist Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum)
CTNT 2022 - An Introduction to Galois Representations (Lecture 1) - by Alvaro Lozano-Robledo
This video is part of a mini-course on "An Introduction to Galois Representations" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - An Introduction to Galois Representations (by Alvaro Lozano-Robledo)
Pierre Emmanuel Caprace - Groups with irreducibly unfaithful subsets for unitary representations
A subset F of a group G is called irreducibly faithful if G has an irreducible unitary representation whose kernel does not contain any non-trivial element of F. We say that G has property P(n) if every subset of size at most n is irreducibly faithful. By a classical result o
From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette
Ralf Meyer: On the classification of group actions on C*-algebras up to equivariant KK-equivalence
Talk by Ralf Meyer in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on November 10, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 4/4
We motivate, define and study Donaldson-Thomas invariants and Cohomological Hall algebras associated to quivers, relate them to the geometry of moduli spaces of quiver representations and (in special cases) to Gromov-Witten invariants, and discuss the algebraic structure of Cohomological H
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
E. Amerik - On the characteristic foliation
Abstract - Let X be a holomorphic symplectic manifold and D a smooth hypersurface in X. Then the restriction of the symplectic form on D has one-dimensional kernel at each point. This distribution is called the characteristic foliation. I shall survey a few results concerning the possible
From playlist Ecole d'été 2019 - Foliations and algebraic geometry
Rings 12 Duality and injective modules
This lecture is part of an online course on rings and modules. We descibe some notions of duality for modules generalizing the dual of a vector space. We first discuss duality for free and projective modules, which is very siilar to the vector space case. Then we discuss duality for finit
From playlist Rings and modules
Recursively Defined Sets - An Intro
Recursively defined sets are an important concept in mathematics, computer science, and other fields because they provide a framework for defining complex objects or structures in a simple, iterative way. By starting with a few basic objects and applying a set of rules repeatedly, we can g
From playlist All Things Recursive - with Math and CS Perspective
algebraic geometry 7 weak nullstellensatz
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It describes the weak nullstellensatz, giving the maximal ideals of polynomial rings over algebraically closed fields.
From playlist Algebraic geometry I: Varieties