Group theory 2: Cayley's theorem
This is lecture 2 of an online mathematics course on group theory. It describes Cayley's theorem that every abstract group is the group of symmetries of something, and as examples shows the Cayley graphs of the Klein 4-group and the symmetric group on 3 points.
From playlist Group theory
Cayley's Theorem Explanation: Every Group is a Permutation Group
Functions with two-sided inverse are bijective: https://youtu.be/XnkgXYvwJZw First isomorphism theorem explanation: https://youtu.be/ssVIJO5uNeg Proof that every group is isomorphic to a subgroup of the symmetric group. We use group actions to derive this very interesting fact in group
From playlist Group Theory
Group theory 4: Lagrange's theorem
This is lecture 4 of an online course on mathematical group theory. It introduces Lagrange's theorem that the order of a subgroup divides the order of a group, and uses it to show that all groups of prime order are cyclic, and to prove Fermat's theorem and Euler's theorem.
From playlist Group theory
Group theory 29:The Jordan Holder theorem
This lecture is part of an online course on group theory. It covers the Jordan-Holder theorem, staring that the simple groups appearing in a composition series of a finite group do not depend on the composition series.
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
We finally get to Lagrange's theorem for finite groups. If this is the first video you see, rather start at https://www.youtube.com/watch?v=F7OgJi6o9po&t=6s In this video I show you how the set that makes up a group can be partitioned by a subgroup and its cosets. I also take a look at
From playlist Abstract algebra
Abstract Algebra | Cayley's Theorem
We state and prove Cayley's theorem. An example related to this theorem is also presented. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
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
Hankyung Ko: A singular Coxeter presentation
SMRI Algebra and Geometry Online Hankyung Ko (Uppsala University) Abstract: A Coxeter system is a presentation of a group by generators and a specific form of relations, namely the braid relations and the reflection relations. The Coxeter presentation leads to, among others, a similar pre
From playlist SMRI Algebra and Geometry Online
Homology cobordism and triangulations – Ciprian Manolescu – ICM2018
Geometry | Topology Invited Lecture 5.5 | 6.1 Homology cobordism and triangulations Ciprian Manolescu Abstract: The study of triangulations on manifolds is closely related to understanding the three-dimensional homology cobordism group. We review here what is known about this group, with
From playlist Geometry
symplectic topology - Lev Buhovsky
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: The Arnold conjecture, spectral invariants and C^0 symplectic topology Speaker: Lev Buhovsky Affiliation: Tel Aviv University Date: October 9, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Richard Hain - 4/4 Universal mixed elliptic motives
Prof. Richard HAIN (Duke University, Durham, USA) Universal mixed elliptic motives are certain local systems over a modular curve that are endowed with additional structure, such as that of a variation of mixed Hodge structure. They form a tannakian category. The coordinate ring of its fu
From playlist Richard Hain - Universal mixed elliptic motives
Richard Hain: Mixed motives associated to elliptic curves
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 Algebraic and Complex Geometry
Second Isomorphism Theorem for Groups Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Second Isomorphism Theorem for Groups Proof. If G is a group and H and K are subgroups of G, and K is normal in G, we prove that H/(H n K) is isomorphic to HK/K.
From playlist Abstract Algebra
Francis Brown - 1/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)
In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of
From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)
Prasad's work on the congruence subgroup problem by Andrei Rapinchuk
PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will
From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)
Ian Montague: Seiberg-Witten Floer K-Theory and Cyclic Group Actions on Spin 4-Manifolds w/ Boundary
Ian Montague, Brandeis University Title: Seiberg-Witten Floer K-Theory and Cyclic Group Actions on Spin 4-Manifolds with Boundary I will outline the construction of a metric-independent $\text{Pin}(2)\widetilde{\times}\mathbb{Z}_{m}$-equivariant Seiberg-Witten Floer spectrum $\text{SWF}(Y)
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Eisenstein Ideals: A Link Between Geometry and Arithmetic - Emmanuel Lecouturier
Short Talks by Postdoctoral Members Topic: Eisenstein Ideals: A Link Between Geometry and Arithmetic Speaker: Emmanuel Lecouturier Affiliation: Member, School of Mathematics Date: September 25, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Chapter 6: Homomorphism and (first) isomorphism theorem | Essence of Group Theory
The isomorphism theorem is a very useful theorem when it comes to proving novel relationships in group theory, as well as proving something is a normal subgroup. But not many people can understand it intuitively and remember it just as a kind of algebraic coincidence. This video is about t
From playlist Essence of Group Theory