Group actions in abstract algebra
In this first video on group actions, I use an example of some previous work on the symmetric group to give you some intuition about group actions. Beware when reading your textbook. It is probably unnecessary difficult just due to the dot notation that is used when describing group acti
From playlist Abstract algebra
Abstract Algebra: Group actions are defined as a formal mechanism that describes symmetries of a set X. A given group action defines an equivalence relation, which in turn yields a partition of X into orbits. Orbits are also described as cosets of the group. U.Reddit course materials a
From playlist Abstract Algebra
In this video I demonstrate an example of a non-faithful group actions, where the identity permutation is actually mapped to by all the elements in the group set. Another example shows you how group actions involving a group set on itself gives rise to group element composition as we see
From playlist Abstract algebra
What is a Group Action? : A Group as a Category and The Skeleton Operation ☠
This week I try to take a more Categorical approach to answering and expanding upon the question of "what is a group action". Along the way I'll go over thinking about a group as a category and eventually hit on the skeleton operation on a category and use it to present an example of the c
From playlist The New CHALKboard
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
Visual Group Theory, Lecture 5.1: Groups acting on sets
Visual Group Theory, Lecture 5.1: Groups acting on sets When we first learned about groups as collections of actions, there was a subtle but important difference between actions and configurations. This is the tip of the iceberg of a more general and powerful concept of a group action. Ma
From playlist Visual Group Theory
Group action proofs in abstract algebra
This video follows from the previous one, in which we developed an intuitive understanding of group actions by way of an example. In this video I want to spend a few minutes on the proofs that connect the elements in a group set with the permutations of another set.
From playlist Abstract algebra
Visual Group Theory, Lecture 5.3: Examples of group actions
Visual Group Theory, Lecture 5.3: Examples of group actions It is frequently of interest to analyze the action of a group on its elements (by multiplication), subgroups (by multiplication, or by conjugation), or cosets (by multiplication). We look at all of these, and analyze the orbits,
From playlist Visual Group Theory
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
Cyril Demarche: Cohomological obstructions to local-global principles - lecture 2
Hasse proved that for quadrics the existence of rational points reduces to the existence of solutions over local fields. In many cases, cohomological constructions provide obstructions to such a local to global principle. The objective of these lectures is to give an introduction to these
From playlist Algebraic and Complex Geometry
Francis Brown - 4/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)
In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of
From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)
A Hecke action on the principal block of a semisimple algebraic group - Simon Riche
Workshop on Representation Theory and Geometry Topic: A Hecke action on the principal block of a semisimple algebraic group Speaker: Simon Riche Affiliation: Université Paris 6; Member, School of Mathematics Date: April 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
David Rydh. Local structure of algebraic stacks and applications
Abstract: Some natural moduli problems, such as moduli of sheaves and moduli of singular curves, give rise to stacks with infinite stabilizers that are not known to be quotient stacks. The local structure theorem states that many stacks locally look like the quotient of a scheme by the act
From playlist CORONA GS
Cyril Demarche: Cohomological obstructions to local-global principles - lecture 4
Hasse proved that for quadrics the existence of rational points reduces to the existence of solutions over local fields. In many cases, cohomological constructions provide obstructions to such a local to global principle. The objective of these lectures is to give an introduction to these
From playlist Algebraic and Complex Geometry
Arithmetic D-modules and locally analytic representations
T. Schmidt (Université de Münster) Arithmetic D-modules and locally analytic representations Conférence de mi-parcours du programme ANR Théorie de Hodge p-adique et Développements (ThéHopaD) 25-27 septembre 2013 Centre de conférences Marilyn et James Simons IHÉS Bures / Yvette France
From playlist Conférence de mi-parcours du programme ANRThéorie de Hodge p-adique et Développements (ThéHopaD)25-27 septembre 2013
Parahoric torsors, parabolic bundles and applications by Vikraman Balaji
DISCUSSION MEETING : MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE : 10 February 2020 to 14 February 2020 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classif
From playlist Moduli Of Bundles And Related Structures 2020
Association schemes and codes II: Completeness of the hierarchy of high-order...-Leonardo Coregliano
Computer Science/Discrete Mathematics Seminar II Topic: Association schemes and codes II: Completeness of the hierarchy of high-order Hamming schemes Speaker: Leonardo Coregliano Affiliation: Member, School of Mathematics Date: May 17, 2022 One of the central problems of coding theory is
From playlist Mathematics
Support Varieties for Modular Representations - Eric M. Friedlander
Members’ Seminar Topic: Support Varieties for Modular Representations Speaker: Eric M. Friedlander Affiliation: University of Southern California; Member, School of Mathematics Date: November 30, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
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