Euclidean geometry | Symmetry | Group theory
A one-dimensional symmetry group is a mathematical group that describes symmetries in one dimension (1D). A pattern in 1D can be represented as a function f(x) for, say, the color at position x. The only nontrivial point group in 1D is a simple reflection. It can be represented by the simplest Coxeter group, A1, [ ], or Coxeter-Dynkin diagram . Affine symmetry groups represent translation. Isometries which leave the function unchanged are translations x + a with a such that f(x + a) = f(x) and reflections a − x with a such that f(a − x) = f(x). The reflections can be represented by the affine Coxeter group [∞], or Coxeter-Dynkin diagram representing two reflections, and the translational symmetry as [∞]+, or Coxeter-Dynkin diagram as the composite of two reflections. (Wikipedia).
Group Theory II Symmetry Groups
Why are groups so popular? Well, in part it is because of their ability to characterise symmetries. This makes them a powerful tool in physics, where symmetry underlies our whole understanding of the fundamental forces. In this introduction to group theory, I explain the symmetry group of
From playlist Foundational Math
The Quaternion Symmetry Group – Vi Hart
From playlist G4G11 Videos
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
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
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
A more high brow video. An introduction to group theory - the mathematics of symmetry. This is what I really study.
From playlist My Maths Videos
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
Simple groups, Lie groups, and the search for symmetry II | Math History | NJ Wildberger
This is the second video in this lecture on simple groups, Lie groups and manifestations of symmetry. During the 19th century, the role of groups shifted from its origin in number theory and the theory of equations to its role in describing symmetry in geometry. In this video we talk abou
From playlist MathHistory: A course in the History of Mathematics
Symmetries in QFT and their Relationship with Category Theory (Lecture 3) by Lakshya Bhardwaj
INFOSYS-ICTS STRING THEORY LECTURES SYMMETRIES IN QFT AND THEIR RELATIONSHIP WITH CATEGORY THEORY SPEAKER: Lakshya Bhardwaj (Mathematical Institute, University of Oxford) DATE : 10 October 2022 to 12 October 2022 VENUE: Madhava Lecture Hall (Hybrid) Lecture 1: 10 October 2022 at 3:30 pm
From playlist Infosys-ICTS String Theory Lectures
Group Theory Package (GTPack) and Symmetry Principles in Condensed Matter: Live with the R&D team
In this stream, we have Group Theory Package (GTPack) and Symmetry Principles in Condensed Matter with Wolfram R&D. Follow us on our official social media channels. Twitter: https://twitter.com/WolframResearch/ Facebook: https://www.facebook.com/wolframresearch/ Instagram: https://
From playlist Live with the R&D Team
Bridges 2014 talk: The quaternion group as a symmetry group
This is a talk I gave at the Bridges conference on mathematics and the arts (http://bridgesmathart.org/), on 18th August 2014, about my paper with Vi Hart with the same title. The slides are available at https://www.math.okstate.edu/~segerman/talks/quaternion_group_as_a_symmetry_group.pdf
From playlist 3D printing
Dominic Else - Emergent Symmetries and Anomalies in Metals: Luttinger's Theorem and Beyond
Séminaire organisé le 23 novembre 2021 Metals are an interesting class of gapless quantum many-body systems. Many metals are described by the famous "Fermi liquid theory" at low temperatures, but there are also many metallic materials for which Fermi liquid theory is an inadequate descrip
From playlist Quantum Encounters Seminar - Quantum Information, Condensed Matter, Quantum Field Theory
Strange Pattern in symmetries - Bott periodicity
A strange repeating pattern in the symmetries of circles, spheres and higher dimensional spheres called Bott periodicity. We will learn about symmetries of spheres, homotopy groups, the orthogonal groups and, finally, Bott periodicity. Produced by Connect films https://www.connectfi
From playlist Summer of Math Exposition Youtube Videos
Anton Kapustin - Higher Symmetry, TQFT, and Gapped Phases of Matter
Anton KAPUSTIN (Caltech, Pasadena, USA)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur
AMMI Course "Geometric Deep Learning" - Lecture 3 (Geometric Priors I) - Taco Cohen
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July-August 2021 by Michael Bronstein (Imperial College/Twitter), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 3: Symmetries • Abstract group
From playlist AMMI Geometric Deep Learning Course - First Edition (2021)
SQCD and Pairs of Pants by Shlomo Razamat
PROGRAM QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
AMMI 2022 Course "Geometric Deep Learning" - Lecture 3 (Geometric Priors I) - Taco Cohen
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 by Michael Bronstein (Oxford), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 3: Symmetries • Abstract groups • Symmetry groups • Gro
From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)
http://www.teachastronomy.com/ A lot of fundamental concepts in physics are based on the idea of symmetry. Symmetry is familiar to us in an aesthetic sense. It often means things that have pleasing proportion, or look the same from every direction, or have a harmonious nature about them.
From playlist 23. The Big Bang, Inflation, and General Cosmology 2
Marcus du Sautoy: Symmetry explained
Marcus Peter Francis du Sautoy is a British mathematician, author, and populariser of science and mathematics. You can view more content of Marcus du Sautoy here: https://www.youtube.com/channel/UCYF21Xc9fSdqVWRxpBAOleQ/featured This video is a clip from the Abel Prize Announcement 2008.
From playlist Popular presentations