Group theory 32: Subgroups of free groups
This lecture is part of an online mathematics course on group theory. We describe subgroups of free groups, show that they are free, calculate the number of generators, and give two examples.
From playlist Group theory
This lecture is part of an online math course on group theory. We review free abelian groups, then construct free (non-abelian) groups, and show that they are given by the set of reduced words, and as a bonus find that they are residually finite.
From playlist Group theory
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
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
This video contains the origins of group theory, the formal definition, and theoretical and real-world examples for those beginning in group theory or wanting a refresher :)
From playlist Summer of Math Exposition Youtube Videos
STPM - Torsion-Freeness of Certain Cohomology Groups of PEL-Type Shimura Varieties - Junecue Suh
Junecue Suh Institute for Advanced Study September 30, 2010 For more videos, visit http://video.ias.edu
From playlist Mathematics
The Role of the Transpose in Free Probability - J.Mingo - Workshop 2 - CEB T3 2017
James Mingo / 26.10.17 The Role of the Transpose in Free Probability: the partial transpose of R-cyclic operators Like tensor independence, free independence gives us rules for doing calculations. With random matrix models, we usually need tensor independence of the entries and some kin
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
E. Peyre - Slopes and distribution of points (part4)
The distribution of rational points of bounded height on algebraic varieties is far from uniform. Indeed the points tend to accumulate on thin subsets which are images of non-trivial finite morphisms. The problem is to find a way to characterise these thin subsets. The slopes introduced by
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Every Group is a Quotient of a Free Group
First isomorphism theorem: https://youtu.be/ssVIJO5uNeg An explanation of a proof that every finite group is a quotient of a free group. A similar proof also applies to infinite groups because we can consider a free group on an infinite number of elements! Group Theory playlist: https://
From playlist Group Theory
James Mingo: The infinitesimal Weingarten calculus
Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: The Weingarten calculus calculates matrix integrals over the unitary and orthogonal groups, in particular their large N behaviour. In this talk we shall look at the W
From playlist Noncommutative geometry meets topological recursion 2021
Groups and subgroups -- Proofs
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Polynomials over ℤ and ℚ: counting and freeness - Timothy Browning
Members' Colloquium Topic: Polynomials over ℤ and ℚ: counting and freeness Speaker: Timothy Browning Affiliation: Member, School of Mathematics Date: October 31, 2022 Humans have been thinking about polynomial equations over the integers, or over the rational numbers, for many years. D
From playlist Mathematics
Sebastian Eterović, UC Berkeley
April 12, Sebastian Eterović, UC Berkeley Existential Closedness and Differential Algebra
From playlist Spring 2022 Online Kolchin seminar in Differential Algebra
Chapter 1: Symmetries, Groups and Actions | Essence of Group Theory
Start of a video series on intuitions of group theory. Groups are often introduced as a kind of abstract algebraic object right from the start, which is not good for developing intuitions for first-time learners. This video series hopes to help you develop intuitions, which are useful in u
From playlist Essence of Group Theory
E. Peyre - Slopes and distribution of points (part3)
The distribution of rational points of bounded height on algebraic varieties is far from uniform. Indeed the points tend to accumulate on thin subsets which are images of non-trivial finite morphisms. The problem is to find a way to characterise these thin subsets. The slopes introduced by
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Dimitri Shlyakhtenko: Free probability of type B and asymptotics of finite-rank perturbations ...
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Analysis and its Applications
From playlist Contributed talks One World Symposium 2020
Group Theory: The Center of a Group G is a Subgroup of G Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Theory: The Center of a Group G is a Subgroup of G Proof
From playlist Abstract Algebra
This is lecture 3 of an online mathematics course on group theory. It gives a review of homomorphisms and isomorphisms and gives some examples of these.
From playlist Group theory
Benson Au: "Finite-rank perturbations of random band matrices via infinitesimal free probability"
Asymptotic Algebraic Combinatorics 2020 "Finite-rank perturbations of random band matrices via infinitesimal free probability" Benson Au - University of California, San Diego (UCSD) Abstract: Free probability provides a unifying framework for studying random multi-matrix models in the la
From playlist Asymptotic Algebraic Combinatorics 2020