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
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
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
Now that we know what quotient groups, a kernel, and normal subgroups are, we can look at the first isomorphism theorem. It states that the quotient group created by the kernel of a homomorphism is isomorphic to the (second) group in the homomorphism.
From playlist Abstract algebra
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
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
Learn the basics for simplifying an expression using the rules of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
Isomorphisms (Abstract Algebra)
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same. Be sure to subscribe s
From playlist Abstract Algebra
Simplify a rational expression by using properties of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
Vincent LAFFORGUE - Stacks of Shtukas and spectral decompositions
https://ams-ems-smf2022.inviteo.fr/
From playlist International Meeting 2022 AMS-EMS-SMF
Zlil Sela - Automorphisms of groups and a higher rank JSJ decomposition
The JSJ (for groups) was originally constructed to study the automorphisms and the cyclic splittings of a (torsion-free) hyperbolic group. Such a structure theory was needed to complete the solution of the isomorphism problem for (torsion-free) hyperbolic groups. Later, the JSJ was genera
From playlist Geometry in non-positive curvature and Kähler groups
Cubic surfaces and non-Euclidean geometry - William Goldman
Members’ Colloquium Topic: Cubic surfaces and non-Euclidean geometry Speaker: William Goldman Affiliation: University of Maryland; Member, School of Mathematics Date: January 24, 2022 The classification of geometric structures on manifolds naturally leads to actions of automorphism group
From playlist Mathematics
Susanna Zimmermann: Signature morphisms from the Cremona group
Abstract: The plane Cremona group is the group of birational transformations of the projective plane. I would like to discuss why over algebraically closed fields there are no homomorphisms from the plane Cremona group to a finite group, but for certain non-closed fields there are (in fact
From playlist Algebraic and Complex Geometry
Karen VOGTMANN - Spaces of Graphs, Tori and Other Flat Gamma-complexes
Spaces of finite graphs play a key role in perturbative quantum field theory, but also in many other areas of science and mathematics. Among these is geometric group theory, where they are used to model groups of automorphism of free groups. Graphs can be thought of as 1-dimensional flat m
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Ana Caraiani - 2/3 Shimura Varieties and Modularity
We describe the Calegari-Geraghty method for proving modularity lifting theorems beyond the classical setting of the Taylor-Wiles method. We discuss the three conjectures that this method relies on (existence of Galois representations, local-global compatibility and vanishing of cohomology
From playlist 2022 Summer School on the Langlands program
GT12.1. Automorphisms of Dihedral Groups
Abstract Algebra: We compute Aut(G), Inn(G), and Out(G) when G is a dihedral group D_2n. We also show that Aut(D_2n) always contains a subgroup isomorphic to D_2n and that Aut(D_2n) may be realized as a matrix group with entries n Z/n.
From playlist Abstract Algebra
Moduli Stacks of Galois Representations by Mathew Emerton
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
Strong approximation for the Markoff equation via nonabelian level structures...- William Chen
Joint IAS/Princeton University Number Theory Seminar Topic: Strong approximation for the Markoff equation via nonabelian level structures on elliptic curves Speaker: William Chen Affiliation: Columbia University Date: November 5, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
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
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