A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.
From playlist Modern Algebra - Chapter 15 (groups)
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
Difference Between Normalizer, Centralizer, and Stabilizer
An easy way to remember what is the normalizer and centralizer of a subgroup, and what is the stabilizer of an element under a group action. For people learning abstract algebra! Group Theory playlist: https://youtube.com/playlist?list=PLug5ZIRrShJHDvvls4OtoBHi6cNnTZ6a6 Subscribe to see
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
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Stable Homotopy Seminar, 8: The Stable Model Category of Spectra
We discuss the enrichment of spectra over spaces, and the compatibility of this enrichment with the model structure. Then we define the stable model structure by adding extra cofibrations to the levelwise model category of spectra, and restricting the weak equivalences to those maps which
From playlist Stable Homotopy Seminar
The idea of a quotient group follows easily from cosets and Lagrange's theorem. In this video, we start with a normal subgroup and develop the idea of a quotient group, by viewing each coset (together with the normal subgroup) as individual mathematical objects in a set. This set, under
From playlist Abstract algebra
Chapter 5: Quotient groups | Essence of Group Theory
Quotient groups is a very important concept in group theory, because it has paramount importance in group homomorphisms (connection with the isomorphism theorem(s)). With this video series, abstract algebra needs not be abstract - one can easily develop intuitions for group theory! In fac
From playlist Essence of Group Theory
Ultrametric stability problems - Francesco Fournier Facio
Stability and Testability Topic: Ultrametric stability problems Speaker: Francesco Fournier Facio Affiliation: Eidgenössische Technische Hochschule Zürich Date: March 31, 2021 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Tasho Kaletha - 1/2 A Brief Introduction to the Trace Formula and its Stabilization
We will discuss the derivation of the stable Arthur-Selberg trace formula. In the first lecture we will focus on anisotropic reductive groups, for which the trace formula can be derived easily. We will then discuss the stabilization of this trace formula, which is unconditional on the geom
From playlist 2022 Summer School on the Langlands program
Endoscopy theory for symplectic and orthogonal similitude groups - Bin Xu
Bin Xu Member, School of Mathematics January 29, 2015 The endoscopy theory provides a large class of examples of Langlands functoriality, and it also plays an important role in the classification of automorphic forms. The central part of this theory are some conjectural identities of Hari
From playlist Mathematics
This organic chemistry video tutorial provides a basic introduction into newman projections. It explains how to draw the newman projections of ethane, butane, and 2,3-dimethylpentane. It explains how to draw the eclipsed and staggered conformations of ethane as well as the gauche and ant
From playlist New Organic Chemistry Playlist
Chair Conformation and Ring Flips
This organic chemistry video tutorial provides a basic introduction into drawing the chair conformation of cyclohexane and identifying the most stable conformation of Methylcyclohexane and 1-tert-butyl-4-methylcyclohexane. It also discusses how to perform a ring flip by adjusting the ap
From playlist New Organic Chemistry Playlist
Organic Chemistry 1 Final Exam Review
This organic chemistry 1 final exam review is for students taking a standardize multiple choice exam at the end of their semester. This review contains plenty of examples and practice problems with solutions covering topics commonly taught in a typical organic chemistry course. Here is a
From playlist New Organic Chemistry Playlist
Stability, testability and property (T) - Oren Beker
Stability and Testability Topic: Stability, testability and property (T) Speaker: Oren Beker Affiliation: University of Cambridge Date: October 28, 2020 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Stability and sofic approximations for product groups and property (tau) - Adrian Ioana
Stability and Testability Topic: Stability and sofic approximations for product groups and property (tau) Speaker: Adrian Ioana Affiliation: University of California, San Diego Date: November 4, 2020 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Quiver moduli and applications, Markus Reineke (Bochum), Lecture 3
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)
Arun Debray - Stable diffeomorphism classification of some unorientable 4-manifolds
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Arun Debray, The University of Texas at Austin Title: Stable diffeomorphism classification of some unorientable 4-manifolds Abstract: Kreck's modified surgery theory provides a bordism-theoretic classification of closed, c
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
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