Jesse Peterson: Von Neumann algebras and lattices in higher-rank groups, Lecture 1
Mini course of the conference YMC*A, August 2021, University of Münster. Lecture 1: Background on von Neumann algebras. Abstract: We’ll briskly review basic properties of semi-finite von Neumann algebras. The standard representation, completely positive maps, group von Neumann algebras, th
From playlist YMC*A 2021
Ring Examples (Abstract Algebra)
Rings are one of the key structures in Abstract Algebra. In this video we give lots of examples of rings: infinite rings, finite rings, commutative rings, noncommutative rings and more! Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦
From playlist Abstract Algebra
This lecture is part of an online course on rings and modules. We prove Hilbert's theorem that poynomial rings over fields are Noetherian, and use this to prove Hilbert's theorem about finite generation of algebras of invariants, at least for finite groups over the complex numbers. For
From playlist Rings and modules
Rigidity for von Neumann algebras – Adrian Ioana – ICM2018
Analysis and Operator Algebras Invited Lecture 8.5 Rigidity for von Neumann algebras Adrian Ioana Abstract: We survey some of the progress made recently in the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces.
From playlist Analysis & Operator Algebras
algebraic geometry 12 Hilbert's finiteness theorem
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the proof of Hilbert's finiteness theorem for rings of invariants. (This is not the same as Hilbert's finiteness theorem for ideals, though the two theorems are
From playlist Algebraic geometry I: Varieties
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
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
8ECM Invited Lecture: Stuart White
From playlist 8ECM Invited Lectures
Logical challenges with abstract algebra II | Abstract Algebra Math Foundations 215 | NJ Wildberger
There is a very big jump in going from finite algebraic objects to "infinite algebraic objects". For example, there is a huge difference, if one is interested in very precise definitions, between the concept of a finite group and the concept of an "infinite group". We illustrate this imp
From playlist Math Foundations
Jamie Gabe: A new approach to classifying nuclear C*-algebras
Talk in the global noncommutative geometry seminar (Europe), 9 February 2022
From playlist Global Noncommutative Geometry Seminar (Europe)
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - D.Farenick
Douglas Farenick (University of Toronto) / 13.09.17 Title: Isometric and Contractive of Channels Relative to the Bures Metric Abstract:In a unital C*-algebra A possessing a faithful trace, the density operators in A are those positive elements of unit trace, and the set of all density el
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Kristin Courtney: "The abstract approach to classifying C*-algebras"
Actions of Tensor Categories on C*-algebras 2021 Mini Course: "The abstract approach to classifying C*-algebras" Kristin Courtney - Westfälische Wilhelms-Universität Münster Institute for Pure and Applied Mathematics, UCLA January 21, 2021 For more information: https://www.ipam.ucla.edu
From playlist Actions of Tensor Categories on C*-algebras 2021
Lauren Ruth: "Von Neumann Equivalence"
Actions of Tensor Categories on C*-algebras 2021 "Von Neumann Equivalence" Lauren Ruth - Mercy College, Mathematics Abstract: We introduce a new equivalence relation on groups, which we call von Neumann equivalence, that is coarser than both measure equivalence and W*-equivalence. Our ge
From playlist Actions of Tensor Categories on C*-algebras 2021
Rolando de Santiago: "L2 cohomology and maximal rigid subalgebras of s-malleable deformations"
Actions of Tensor Categories on C*-algebras 2021 "L2 cohomology and maximal rigid subalgebras of s-malleable deformations" Rolando de Santiago - Purdue University, Department of Mathematics Abstract: A major theme in the study of von Neumann algebras is to investigate which structural as
From playlist Actions of Tensor Categories on C*-algebras 2021
Proof: Ideal of a Ring is Proper iff it has no Units | Abstract Algebra
An ideal of a ring with identity is proper if and only if the ideal contains no units of the ring. We prove this result in today's abstract algebra video lesson! Remember that an ideal, I, of a ring, R, is an additive subgroup of I such that for all r in R and x in I, r*x and x*r are also
From playlist Abstract Algebra
RNT1.2. Definition of Integral Domain
Ring Theory: We consider integral domains, which are commutative rings that contain no zero divisors. We show that this property is equivalent to a cancellation law for the ring. Finally we note some basic connections between integral domains and fields.
From playlist Abstract Algebra
Stefaan Vaes: "Outer actions of amenable groups on von Neumann algebras"
Actions of Tensor Categories on C*-algebras 2021 Mini Course: "Outer actions of amenable groups on von Neumann algebras" Stefaan Vaes - KU Leuven Abstract: I will give a survey lecture on the classification of outer actions of amenable groups on von Neumann algebras with the main focus b
From playlist Actions of Tensor Categories on C*-algebras 2021