301.5A Permutation Groups: Intro and Goals
Goals for studying the properties of permutation groups. Plus, anagrams!
From playlist Modern Algebra - Chapter 16 (permutations)
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From playlist Modern Algebra - Chapter 16 (permutations)
Group theory 15:Groups of order 12
This lecture is part of an online mathematics course on group theory. It uses the Sylow theorems to classify the groups of order 12, and finds their subgroups.
From playlist Group theory
Group theory 13: Dihedral groups
This lecture is part of an online mathematics course on group theory. It covers some basic properties of dihedral groups.
From playlist Group theory
301.5C Definition and "Stack Notation" for Permutations
What are permutations? They're *bijective functions* from a finite set to itself. They form a group under function composition, and we use "stack notation" to denote them in this video.
From playlist Modern Algebra - Chapter 16 (permutations)
Lie Groups and Lie Algebras: Lesson 45 Group Theory Review #4
Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The software I usually use to produce the lectures is: https://apps.apple.com/us/app/vittle-pro-video-whiteboard/id629037418
From playlist Lie Groups and Lie Algebras
Permutation Groups and Symmetric Groups | Abstract Algebra
We introduce permutation groups and symmetric groups. We cover some permutation notation, composition of permutations, composition of functions in general, and prove that the permutations of a set make a group (with certain details omitted). #abstractalgebra #grouptheory We will see the
From playlist Abstract Algebra
Group theory 28: Groups of order 120, 168
This lecture is part of an online math course on group theory. It discusses some examples of groups of order 120 or 168: the binary icosahedral group, the symmetric group, and the symmetries of the Fano plane.
From playlist Group theory
Learning from ranks, learning to rank - Jean-Philippe Vert, Google Brain
Permutations and sorting operators are ubiquitous in data science, e.g., when one wants to analyze or predict preferences. As discrete combinatorial objects, permutations do not lend themselves easily to differential calculus, which underpins much of modern machine learning. In this talk I
From playlist Statistics and computation
Learning from permutations. - Vert - Workshop 3 - CEB T1 2019
Jean-Philippe Vert (Mines ParisTech, Google) / 05.04.2019 Learning from permutations. Changes in image quality or illumination may affect the pixel intensities, without affecting the relative intensities, i.e., the ranking of pixels in an image by decreasing intensity. In order to learn
From playlist 2019 - T1 - The Mathematics of Imaging
Harald Helfgott: The diameter of the symmetric group: ideas and tools
Abstract: Given a finite group G and a set A of generators, the diameter diam(Γ(G,A)) of the Cayley graph Γ(G,A) is the smallest ℓ such that every element of G can be expressed as a word of length at most ℓ in A∪A−1. We are concerned with bounding diam(G):=maxA diam(Γ(G,A)). It has long be
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi
Christian Gaetz: "Antichains and intervals in the weak order"
Asymptotic Algebraic Combinatorics 2020 "Antichains and intervals in the weak order" Christian Gaetz - Massachusetts Institute of Technology Abstract: The weak order is the partial order on the symmetric group S_n (or other Coxeter group) whose cover relations correspond to simple transp
From playlist Asymptotic Algebraic Combinatorics 2020
Vertex gluings and Demazure products by Nathan Pflueger
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
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
Jean Phillippe Vert: Learning on the symmetric group
Abstract: Many data can be represented as rankings or permutations, raising the question of developing machine learning models on the symmetric group. When the number of items in the permutations gets large, manipulating permutations can quickly become computationally intractable. I will d
From playlist Probability and Statistics
Permutation Orbifolds of Vertex Operator Algebras
This is a recording of a talk I gave at the Illinois State University Algebra Seminar. Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Websi
From playlist Research Talks
Charles Dunkl: Nonsymmetric Jack and Macdonald superpolynomials
HYBRID EVENT Recorded during the meeting "Modern Analysis Related to Root Systems with Applications" the October 18, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathe
From playlist Virtual Conference
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
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
Eric Rowell - Classification of Modular Fusion Categories, Part 2 of 2 - IPAM at UCLA
Recorded 31 August 2021. Eric Rowell of Texas A&M University, College Station, presents "Classification of Modular Fusion Categories" at IPAM's Graduate Summer School: Mathematics of Topological Phases of Matter. This is the second of two talks that Eric presented. Abstrat: Most properties
From playlist Graduate Summer School 2021: Mathematics of Topological Phases of Matter