Group automorphisms in abstract algebra
Group automorphisms are bijective mappings of a group onto itself. In this tutorial I define group automorphisms and introduce the fact that a set of such automorphisms can exist. This set is proven to be a subgroup of the symmetric group. You can learn more about Mathematica on my Udem
From playlist Abstract algebra
Visual Group Theory, Lecture 6.2: Field automorphisms
Visual Group Theory, Lecture 6.2: Field automorphisms A field automorphism is a structure preserving map from a field F to itself. This means that it must be both a homomorphism of both the addtive group (F,+) and the multiplicative group (F-{0},*). We show that any automorphism of an ext
From playlist Visual Group Theory
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Abstract Algebra - 6.5 Automorphisms
We finish up chapter 6 by discussion automorphisms and inner automorphisms. An automorphism is just a special isomorphism that maps a group to itself. An inner-automorphism uses conjugation of an element and its inverse to create a mapping. Video Chapters: Intro 0:00 What is an Automorphi
From playlist Abstract Algebra - Entire Course
In this tutorial I present the cyclic group of three elements as a group automorphism. You can learn more about Mathematica on my Udemy courses: https://www.udemy.com/mathematica/ https://www.udemy.com/mathematica-for-statistics/
From playlist Abstract algebra
Graph Theory FAQs: 02. Graph Automorphisms
An automorphism of a graph G is an isomorphism between G and itself. The set of automorphisms of a graph forms a group under the operation of composition and is denoted Aut(G). The automorphisms of a graph describe the symmetries of the graph. We look at a few examples of graphs and det
From playlist Graph Theory FAQs
Visual Group Theory, Lecture 4.6: Automorphisms
Visual Group Theory, Lecture 4.6: Automorphisms An automorphism is an isomorphism from a group to itself. The set of all automorphisms of G forms a group under composition, denoted Aut(G). After a few simple examples, we learn how Aut(Z_n) is isomorphic to U(n), which is the group consist
From playlist Visual Group Theory
Automorphism groups and modular arithmetic
Jacob explains the concept of the automorphism group of a group, as well as how such groups give rise to useful properties of multiplication in modular arithmetic, including Fermat's Little Theorem.
From playlist Basics: Group Theory
Group Isomorphisms in Abstract Algebra
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Isomorphisms in Abstract Algebra - Definition of a group isomorphism and isomorphic groups - Example of proving a function is an Isomorphism, showing the group of real numbers under addition is isomorphic to the group of posit
From playlist Abstract Algebra
Measure Equivalence, Negative Curvature, Rigidity (Lecture 3) by Camille Horbez
PROGRAM: PROBABILISTIC METHODS IN NEGATIVE CURVATURE ORGANIZERS: Riddhipratim Basu (ICTS - TIFR, India), Anish Ghosh (TIFR, Mumbai, India), Subhajit Goswami (TIFR, Mumbai, India) and Mahan M J (TIFR, Mumbai, India) DATE & TIME: 27 February 2023 to 10 March 2023 VENUE: Madhava Lecture Hall
From playlist PROBABILISTIC METHODS IN NEGATIVE CURVATURE - 2023
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
Degenerations of Kahler forms on K3 surfaces, and some dynamics - Simion Filip
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Degenerations of Kahler forms on K3 surfaces, and some dynamics Speaker: Simion Filip Date: June 04, 2021 K3 surfaces have a rich geometry and admit interesting holomorphic automorphisms. As examples of Calabi-Yau ma
From playlist Mathematics
Karen Vogtmann: The geometry and topology of automorphism groups of free groups
HYBRID EVENT Recorded during the meeting "Groups Acting on Fractals" the April 11, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Ma
From playlist Topology
J. Aramayona - MCG and infinite MCG (Part 3)
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 secon
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Canonical forms for free group automorphisms - Jean Pierre Mutanguha
Arithmetic Groups Topic: Canonical forms for free group automorphisms Speaker: Jean Pierre Mutanguha Affiliation: Member, School of Mathematics Date: March 23, 2022 The Nielsen-Thurston theory of surface homeomorphism can be thought of as a surface analogue to the Jordan Canonical Form.
From playlist Mathematics
Louis Funar : Automorphisms of curve and pants complexes in profinite content
Pants complexes of large surfaces were proved to be vigid by Margalit. We will consider convergence completions of curve and pants complexes and show that some weak four of rigidity holds for the latter. Some key tools come from the geometry of Deligne Mumford compactification of moduli sp
From playlist Topology
Lecture 7: From Equivariance to Naturality - Pim de Haan
Video recording of the First Italian School on Geometric Deep Learning held in Pescara in July 2022. Slides: https://www.sci.unich.it/geodeep2022/slides/2022-07-27%20Naturality%20@%20First%20Italian%20GDL%20Summer%20School.pdf
From playlist First Italian School on Geometric Deep Learning - Pescara 2022
Automorphisms of K3 surfaces – Serge Cantat – ICM2018
Dynamical Systems and Ordinary Differential Equations | Algebraic and Complex Geometry Invited Lecture 9.13 | 4.12 Automorphisms of K3 surfaces Serge Cantat Abstract: Holomorphic diffeomorphisms of K3 surfaces have nice dynamical properties. I will survey the main theorems concerning the
From playlist Algebraic & Complex Geometry
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra