Group theory 17: Finite abelian groups
This lecture is part of a mathematics course on group theory. It shows that every finitely generated abelian group is a sum of cyclic groups. Correction: At 9:22 the generators should be g, h+ng not g, g+nh
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
Jacob explains the fundamental concepts in group theory of what groups and subgroups are, and highlights a few examples of groups you may already know. Abelian groups are named in honor of Niels Henrik Abel (https://en.wikipedia.org/wiki/Niels_Henrik_Abel), who pioneered the subject of
From playlist Basics: Group Theory
Every Group of Order Five or Smaller is Abelian Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Every Group of Order Five or Smaller is Abelian Proof. In this video we prove that if G is a group whose order is five or smaller, then G must be abelian.
From playlist Abstract Algebra
Before we carry on with our coset journey, we need to discover when the left- and right cosets are equal to each other. The obvious situation is when our group is Abelian. The other situation is when the subgroup is a normal subgroup. In this video I show you what a normal subgroup is a
From playlist Abstract algebra
Visual Group Theory, Lecture 4.4: Finitely generated abelian groups
Visual Group Theory, Lecture 4.4: Finitely generated abelian groups We begin this lecture by proving that the cyclic group of order n*m is isomorphic to the direct product of cyclic groups of order n and m if and only if gcd(n,m)=1. Then, we classify all finite abelian groups by decomposi
From playlist Visual Group Theory
Group theory 18: Nilpotent groups
This lecture is part of an online mathematics course on group theory. It lists the groups of order 16, and shows that a finite group is nilpotent if and only if it is a product of p-groups.
From playlist Group theory
Every Subgroup of an Abelian Group is Normal Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Every Subgroup of an Abelian Group is Normal Proof
From playlist Abstract Algebra
Abstract Algebra - 11.1 Fundamental Theorem of Finite Abelian Groups
We complete our study of Abstract Algebra in the topic of groups by studying the Fundamental Theorem of Finite Abelian Groups. This tells us that every finite abelian group is a direct product of cyclic groups of prime-power order. Video Chapters: Intro 0:00 Before the Fundamental Theorem
From playlist Abstract Algebra - Entire Course
Rachel Pries - The geometry of p-torsion stratifications of the moduli space of curve
The geometry of p-torsion stratifications of the moduli space of curve
From playlist 28ème Journées Arithmétiques 2013
Christelle Vincent, Exploring angle rank using the LMFDB
VaNTAGe Seminar, February 15, 2022 License: CC-NC-BY-SA Links to some of the papers mentioned in the talk: Dupuy, Kedlaya, Roe, Vincent: https://arxiv.org/abs/2003.05380 Dupuy, Kedlaya, Zureick-Brown: https://arxiv.org/abs/2112.02455 Zarhin 1979: https://link.springer.com/article/10.100
From playlist Curves and abelian varieties over finite fields
Taylor Dupuy (Nov. 13, 2020): Abelian Varieties Over Finite Fields in the LMFDB
I will talk about things around the LMFDB database of isogeny classes of abelian varieties over finite fields (and maybe even about isomorphism classes). These could include: --"Sato-Ain't" distributions, --weird Tate classes, --Bizzaro Hodge co-levels (and very strange Ax-Katz/Cheval
From playlist Seminar Talks
Edgar Costa, From counting points to rational curves on K3 surfaces
VaNTAGe Seminar, Jan 26, 2021
From playlist Arithmetic of K3 Surfaces
Homotopy of Character Varieties by Sean Lawton
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Karen Vogtmann - On the cohomological dimension of automorphism groups of RAAGs
The class of right-angled Artin groups (RAAGs) includes free groups and free abelian groups, Both of these have extremely interesting automorphism groups, which share some properties and not others. We are interested in automorphism groups of general RAAGs, and in particular
From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette
The Geometric Langlands conjecture and non-abelian Hodge theory (Lecture 3) by Ron Donagi
Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries
From playlist Quantum Fields, Geometry and Representation Theory
We give a buttload of definitions for morphisms on various categories of complexes. The derived category of an abelian category is a category whose objects are cochain complexes and whose morphisms I describe in this video.
From playlist Derived Categories
Introduction to elliptic curves and BSD Conjecture by Sujatha Ramadorai
12 December 2016 to 22 December 2016 VENUE Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution. An
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture