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
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)
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
Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-
From playlist Abstract Algebra
Visual Group Theory, Lecture 1.6: The formal definition of a group
Visual Group Theory, Lecture 1.6: The formal definition of a group At last, after five lectures of building up our intuition of groups and numerous examples, we are ready to present the formal definition of a group. We conclude by proving several basic properties that are not built into t
From playlist Visual Group Theory
This is lecture 5 of an online mathematics course on group theory. It classifies groups of order 4 and gives several examples of products of groups.
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
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 is lecture 1 of an online mathematics course on group theory. This lecture defines groups and gives a few examples of them.
From playlist Group theory
CTNT 2020 - Heuristics for narrow class groups - Benjamin Breen
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Conference Videos
CTNT 2018 - "Arithmetic Statistics" (Lecture 3) by Álvaro Lozano-Robledo
This is lecture 3 of a mini-course on "Arithmetic Statistics", taught by Álvaro Lozano-Robledo, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2018 - "Arithmetic Statistics" by Álvaro Lozano-Robledo
G. Lusztig - Stratifying reductive groups
We define a decomposition of a reductive group into finitely many strata. The largest stratum is the set of regular elements, the smallest stratum is the centre.
From playlist Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday
Anderson Vera - A double Johnson filtration for the mapping class group
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Anderson Vera, Pohang University of Science and Technology (POSTECH - BK21 FOUR Mathematical Sciences Division) Title: A double Johnson filtration for the mapping class group and the Goeritz group of the sphere Abstract: I
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
GT18. Conjugacy and The Class Equation
Abstract Algebra: We consider the group action of the group G on itself given by conjugation. The orbits, called conjugacy classes, partition the group, and we have the Class Equation when G is finite. We also show that the partition applies to normal subgroups. Finally we apply the cla
From playlist Abstract Algebra
J. Aramayona - MCG and infinite MCG (Part 1)
The first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston classification, abelianization, isomorphic rigidity, geometry of combinatorial models. In the second
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Lie Groups and Lie Algebras: Lesson 35 - The Fundamental Group
Lie Groups and Lie Algebras: Lesson 35 - The Fundamental Group Now that we understand the notion of homotopic paths ina topological space, we focus on loops. Using the fact that homotopy is an equivalence relation we create a set of equivalence classes of homotopic loops. That set is give
From playlist Lie Groups and Lie Algebras
Zlil Sela - Envelopes and equivalence relations in a free group
Zlil Sela (Hebrew University of Jerusalem, Israel) We study and classify all the definable equivalence relations in a free (and a torsion-free hyperbolic) group. To do that we associate a Diophantine set with every definable set, that contains the definable set, and its generic points are
From playlist T1-2014 : Random walks and asymptopic geometry of groups.
"Introduction to p-adic harmonic analysis" James Arthur, University of Toronto [2008]
James Arthur, University of Toronto Introduction to harmonic analysis on p-adic groups Tuesday Aug 12, 2008 11:00 - 12:00 The stable trace formula, automorphic forms, and Galois representations Video taken from: http://www.birs.ca/events/2008/summer-schools/08ss045/videos/watch/200808121
From playlist Mathematics
Group theory 20: Frobenius groups
This lecture is part of an online mathematics course on group theory. It gives several examples of Frobenius groups (permutation groups where any element fixing two points is the identity).
From playlist Group theory