Definition of a Ring and Examples of Rings
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Ring and Examples of Rings - Definition of a Ring. - Definition of a commutative ring and a ring with identity. - Examples of Rings include: Z, Q, R, C under regular addition and multiplication The Ring of all n x
From playlist Abstract Algebra
Representation theory: Introduction
This lecture is an introduction to representation theory of finite groups. We define linear and permutation representations, and give some examples for the icosahedral group. We then discuss the problem of writing a representation as a sum of smaller ones, which leads to the concept of irr
From playlist Representation theory
Ring Theory: We define rings and give many examples. Items under consideration include commutativity and multiplicative inverses. Example include modular integers, square matrices, polynomial rings, quaternions, and adjoins of algebraic and transcendental numbers.
From playlist Abstract Algebra
RT6. Representations on Function Spaces
Representation Theory: We note how to transfer a group action of a group G on a set X to a group action on F(X), the functions on X. Because F(X) is a vector space, we obtain a representation of the group, and we can apply previous techniques. In particular, the group acts on itself in
From playlist Representation Theory
Ring Definition (expanded) - Abstract Algebra
A ring is a commutative group under addition that has a second operation: multiplication. These generalize a wide variety of mathematical objects like the integers, polynomials, matrices, modular arithmetic, and more. In this video we will take an in depth look at the definition of a rin
From playlist Abstract Algebra
RT1: Representation Theory Basics
Representation Theory: We present basic concepts about the representation theory of finite groups. Representations are defined, as are notions of invariant subspace, irreducibility and full reducibility. For a general finite group G, we suggest an analogue to the finite abelian case, whe
From playlist *** The Good Stuff ***
RNT1.4. Ideals and Quotient Rings
Ring Theory: We define ideals in rings as an analogue of normal subgroups in group theory. We give a correspondence between (two-sided) ideals and kernels of homomorphisms using quotient rings. We also state the First Isomorphism Theorem for Rings and give examples.
From playlist Abstract Algebra
Visual Group Theory, Lecture 7.1: Basic ring theory
Visual Group Theory, Lecture 7.1: Basic ring theory A ring is an abelian group (R,+) with a second binary operation, multiplication and the distributive law. Multiplication need not commute, nor need there be multiplicative inverses, so a ring is like a field but without these properties.
From playlist Visual Group Theory
Units in a Ring (Abstract Algebra)
The units in a ring are those elements which have an inverse under multiplication. They form a group, and this “group of units” is very important in algebraic number theory. Using units you can also define the idea of an “associate” which lets you generalize the fundamental theorem of ar
From playlist Abstract Algebra
Local (\ell = p) Galois Deformation Rings - Ashwin Iyengar
Joint IAS/Princeton University Number Theory Seminar Topic: Local (\ell = p) Galois Deformation Rings Speaker: Ashwin Iyengar Affiliation: Johns Hopkins University Date: February 10, 2022 I will present joint work with V. Paškūnas and G. Böckle concerning deformation rings for mod p Galo
From playlist Mathematics
Automorphy: Deformations of Galois Representations - David Geraghty
David Geraghty Institute for Advanced Study February 24, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
On the long-term dynamics of nonlinear dispersive evolution equations - Wilhelm Schlag
Analysis Seminar Topic: On the long-term dynamics of nonlinear dispersive evolution equations Speaker: Wilhelm Schlag Affiliation: University of Chicago Visiting Professor, School of Mathematics Date: Febuary 14, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Automorphy: Deformations of Galois Representations (continued) - David Geraghty
David Geraghty Princeton University; Institute for Advanced Study March 3, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Galois Representations 5 by Shaunak Deo
PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA
From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)
Automorphy: Automorphy Lifting Theorems I - David Geraghty
David Geraghty Princeton University; Institute for Advanced Study March 3, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Toby Gee - 2/4 An Introduction to the Categorical p-adic Langlands (...)
An introduction to the ``categorical'' approach to the p-adic Langlands program, in both the ``Banach'' and ``analytic'' settings. Matthew Emerton (Chicago Univ.) Toby Gee (Imperial College) Eugen Hellman (Univ. Münster)
From playlist 2022 Summer School on the Langlands program
Moduli of Representations and Pseudorepresentations - Carl Wang Erickson
Carl Wang Erickson Harvard University May 2, 2013 A continuous representation of a profinite group induces a continuous pseudorepresentation, where a pseudorepresentation is the data of the characteristic polynomial coefficients. We discuss the geometry of the resulting map from the moduli
From playlist Mathematics
Automorphy Lifting for Galois Representations With Small Residual Image - Jack Thorne
Jack Thorne Harvard University February 3, 2011 GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR For more videos, visit http://video.ias.edu
From playlist Mathematics
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 1/4
We motivate, define and study Donaldson-Thomas invariants and Cohomological Hall algebras associated to quivers, relate them to the geometry of moduli spaces of quiver representations and (in special cases) to Gromov-Witten invariants, and discuss the algebraic structure of Cohomological H
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Abstract Algebra: The definition of a Ring
Learn the definition of a ring, one of the central objects in abstract algebra. We give several examples to illustrate this concept including matrices and polynomials. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We recommend th
From playlist Abstract Algebra