In this video we construct a symmetric group from the set that contains the six permutations of a 3 element group under composition of mappings as our binary operation. The specifics topics in this video include: permutations, sets, groups, injective, surjective, bijective mappings, onto
From playlist Abstract algebra
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Visual Group Theory, Lecture 2.2: Dihedral groups
Cyclic groups describe the symmetry of objects that exhibit only rotational symmetry, like a pinwheel. Dihedral groups describe the symmetry of objects that exhibit rotational and reflective symmetry, like a regular n-gon. The corresponding dihedral group D_n has 2n elements: half are rota
From playlist Visual Group Theory
Bireflections (Geometric Algebra 1.3)
In the third video of the series we need to have a chat about reflections. They are the atoms of transformations: a single reflection is a discrete transformation of space, but the product of two reflections is a continuous transformation. When the two reflections intersect they generate a
From playlist Bivector.net
Physics 11.1.3a - Spherical and Parabolic Mirrors
Spherical and Parabolic mirrors. From the Physics course by Derek Owens. The distance learning class is available at www.derekowens.com
From playlist Physics - Reflection and Refraction
Light and Optics 1_2 Introduction to Reflection
Reflection form plane and spherical mirrors
From playlist Physics - Light and Optics
Michael Wibmer: Etale difference algebraic groups
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
Visual Group Theory, Lecture 2.3: Symmetric and alternating groups
Visual Group Theory, Lecture 2.3: Symmetric and alternating groups In this lecture, we introduce the last two of our "5 families" of groups: (4) symmetric groups and (5) alternating groups. The symmetric group S_n is the group of all n! permutations of {1,...,n}. We see several different
From playlist Visual Group Theory
Tathagata Basak: A monstrous(?) complex hyperbolic orbifold
I will report on progress with Daniel Allcock on the ”Monstrous Proposal”, namely the conjecture: Complex hyperbolic 13-space, modulo a particular discrete group, and with orbifold structure changed in a simple way, has fundamental group equal to (MxM)(semidirect)2, where M is the Monster
From playlist Topology
John R. Parker: Complex hyperbolic lattices
Lattices in SU(2,1) can be viewed in several different ways: via their geometry as holomorphic complex hyperbolic isometries, as monodromy groups of hypergeometric functions, via algebraic geometry as ball quotients and (sometimes) using arithmeticity. In this talk I will describe these di
From playlist Geometry
On Ultra-Parallel Complex Hyperbolic Triangle Groups by Anna Pratoussevitch
SURFACE GROUP REPRESENTATIONS AND GEOMETRIC STRUCTURES DATE: 27 November 2017 to 30 November 2017 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classi
From playlist Surface Group Representations and Geometric Structures
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
Geometric Categorifications of the Hecke Algebra - Laura Rider
2021 Women and Mathematics Colloquium Topic: Geometric Categorifications of the Hecke Algebra Speaker: Laura Rider Affiliation: University of Georgia Date: May 26, 2021 In the first part of this talk, I'll explain a geometric categorification of the Hecke algebra in terms of perverse sh
From playlist Mathematics
Yuri Berest : Spaces of quasi-invariants
CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 26, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR
From playlist Topology
GT5. Index 2 Theorem and Dihedral Groups
EDIT: typo at 12:00, it should be "0 less than/equals k less than n", so as to include e and C. Abstract Algebra: We state and prove the Index Two Theorem for finding normal subgroup and list several examples. These include S3, A4, and the symmetry groups for the regular n-gon, D_2n.
From playlist Abstract Algebra
Complex hyperbolic representations of triangle groups by John Parker
SURFACE GROUP REPRESENTATIONS AND GEOMETRIC STRUCTURES DATE: 27 November 2017 to 30 November 2017 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classi
From playlist Surface Group Representations and Geometric Structures
Vic Reiner, Lecture II - 11 February 2015
Vic Reiner (University of Minnesota) - Lecture II http://www.crm.sns.it/course/4036/ Many results in the combinatorics and invariant theory of reflection groups have q-analogues for the finite general linear groups GLn(Fq). These lectures will discuss several examples, and open questions
From playlist Algebraic topology, geometric and combinatorial group theory - 2015
Abstract Algebra | The dihedral group
We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra