Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
Group theory 32: Subgroups of free groups
This lecture is part of an online mathematics course on group theory. We describe subgroups of free groups, show that they are free, calculate the number of generators, and give two examples.
From playlist Group theory
This lecture is part of an online math course on group theory. We review free abelian groups, then construct free (non-abelian) groups, and show that they are given by the set of reduced words, and as a bonus find that they are residually finite.
From playlist Group theory
Every Group is a Quotient of a Free Group
First isomorphism theorem: https://youtu.be/ssVIJO5uNeg An explanation of a proof that every finite group is a quotient of a free group. A similar proof also applies to infinite groups because we can consider a free group on an infinite number of elements! Group Theory playlist: https://
From playlist Group Theory
What is a Group? | Abstract Algebra
Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s
From playlist Abstract Algebra
Visual Group Theory, Lecture 3.4: Direct products
Visual Group Theory, Lecture 3.4: Direct products There is a natural way to put a group structure on the Cartesian product of two groups. In this lecture, we introduce this concept algebraically, and show several different ways to visualize this, using tools such as Cayley diagrams and mu
From playlist Visual Group Theory
Abstract Algebra | Internal direct product of subgroups.
We give the definition of an internal direct product of subgroups, prove a result, and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Visual Group Theory, Lecture 3.5: Quotient groups
Visual Group Theory, Lecture 3.5: Quotient groups Like how a direct product can be thought of as a way to "multiply" two groups, a quotient is a way to "divide" a group by one of its subgroups. We start by defining this in terms of collapsing Cayley diagrams, until we get a conjecture abo
From playlist Visual Group Theory
Invariant Measures for Horospherical Flows by Hee Oh
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
Abstract Algebra: We consider conditions for when a group is isomorphic to a direct or semidirect product. Examples include groups of order 45, 21, and cyclic groups Z/mn, where m,n are relatively prime. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-grou
From playlist Abstract Algebra
From graph limits to higher order Fourier analysis – Balázs Szegedy – ICM2018
Combinatorics Invited Lecture 13.8 From graph limits to higher order Fourier analysis Balázs Szegedy Abstract: The so-called graph limit theory is an emerging diverse subject at the meeting point of many different areas of mathematics. It enables us to view finite graphs as approximation
From playlist Combinatorics
Martin Bridson - Subgroups of direct products of surface groups
After reviewing what is known about subgroups of direct products of surface groups and their significance in the story of which groups are Kähler, I shall describe a new construction that provides infinite families of finitely presented subgroups. These subgroups have varying higher-finite
From playlist Geometry in non-positive curvature and Kähler groups
Rings 10 Tensor products of abelian groups
This lecture is part of an online course on rings and modules. We define tensor products of abelian groups, and calculate them for many common examples using the fact that tensor products preserve colimits. For the other lectures in the course see https://www.youtube.com/playlist?list=P
From playlist Rings and modules
Stability and Invariant Random Subgroups - Henry Bradford
Stability and Testability Topic: Stability and Invariant Random Subgroups Speaker: Henry Bradford Affiliation: Cambridge University Date: January 20, 2021 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Stability of amenable groups via ergodic theory - Arie Levit
Stability and Testability Topic: Stability of amenable groups via ergodic theory Speaker: Arie Levit Affiliation: Yale University Date: January 27, 2021 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Discrete Isometry Group of Higher Rank Symmetric Spaces (Lecture - 02) by Misha Kapovich
Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b
From playlist Geometry, Groups and Dynamics (GGD) - 2017
Rings 13 Colimits and exactness
This lecture is part of an online course on rings and modules. We discuss the problem of when a colimit of exact sequences is exact. We show that the colimit of exact sequences is at least right exact, but give an example to show that it is not always left exact. We find some conditions u
From playlist Rings and modules
Nonetheless one should learn the language of topos: Grothendieck... - Colin McLarty [2018]
Grothendieck's 1973 topos lectures Colin McLarty 3 mai 2018 In the summer of 1973 Grothendieck lectured on several subjects in Buffalo NY, and these lectures were recorded, including 33 hours on topos theory. The topos lectures were by far the most informal of the series, with the most si
From playlist Number Theory
Groups and subgroups -- Proofs
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
CTNT 2022 - An Introduction to Galois Representations (Lecture 2) - 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)