Groups with bounded generation: old and new - Andrei S. Rapinchuk
Joint IAS/Princeton University Number Theory Seminar Topic: Groups with bounded generation: old and new Speaker: Andrei S. Rapinchuk Date: May 06, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-
From playlist Abstract Algebra
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
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
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
Groups with bounded generation: properties and examples - Andrei S. Rapinchuk
Arithmetic Groups Topic: Groups with bounded generation: properties and examples Speaker: Andrei S. Rapinchuk Affiliation: University of Virginia Date: October 20, 2021 After surveying some important consequences of the property of bounded generation (BG) dealing with SS-rigidity, the co
From playlist Mathematics
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
Word width in higher rank arithmetic groups - Chen Meiri
Special Year Research Seminar Topic: Word width in higher rank arithmetic groups Speaker: Chen Meiri Affiliation: Technion - Israel Institute of Technology Date: October 18, 2022 A word on d letters is an element of the free group of rank d, say, with basis x_1,…,x_d. Given a word w=w(x_
From playlist Mathematics
Cyclic groups and finite groups
Jacob goes into detail on some particularly important finite groups, and explains how groups and subgroups can be generated by their elements, along with some important consequences.
From playlist Basics: Group Theory
Denis Osin: Acylindrically hyperbolic groups (part 1)
The lecture was held within the framework of Follow-up Workshop TP Rigidity. 28.4.2015
From playlist HIM Lectures 2015
The idea of a quotient group follows easily from cosets and Lagrange's theorem. In this video, we start with a normal subgroup and develop the idea of a quotient group, by viewing each coset (together with the normal subgroup) as individual mathematical objects in a set. This set, under
From playlist Abstract algebra
Miroslav Englis: Analytic continuation of Toeplitz operators
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
Every Compact Set in n space is Bounded
Every Compact Set in n space is Bounded If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Advanced Calculus
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
Metric embeddings, uniform rectifiability, and the Sparsest Cut problem - Robert Young
Members' Seminar Topic: Metric embeddings, uniform rectifiability, and the Sparsest Cut problem Speaker: Robert Young Affiliation: New York University; von Neumann Fellow, School of Mathematics Date: November 2, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Acylindrically hyperbolic structures on groups - Balasubramanya
Women and Mathematics Title: Acylindrically hyperbolic structures on groups Speaker: Sahana Hassan Balasubramanya Affiliation: Vanderbilt University Date: May 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Zlil Sela - Envelopes and equivalence relations in a free group
Zlil Sela (Hebrew University of Jerusalem, Israel) We study and classify all the definable equivalence relations in a free (and a torsion-free hyperbolic) group. To do that we associate a Diophantine set with every definable set, that contains the definable set, and its generic points are
From playlist T1-2014 : Random walks and asymptopic geometry of groups.