This lecture is part of an online graduate course on Lie groups. We define the Lie algebra of a Lie group in two ways, and show that it satisfied the Jacobi identity. The we calculate the Lie algebras of a few Lie groups. For the other lectures in the course see https://www.youtube.co
From playlist Lie groups
In this video I write down the axioms of Lie algebras and then discuss the defining anti-symmetric bilinear map (the Lie bracket) which is zero on the diagonal and fulfills the Jacobi identity. I'm following the compact book "Introduction to Lie Algebras" by Erdmann and Wildon. https://gi
From playlist Algebra
This lecture is part of an online graduate course on Lie groups. We give an introductory survey of Lie groups theory by describing some examples of Lie groups in low dimensions. Some recommended books: Lie algebras and Lie groups by Serre (anything by Serre is well worth reading) Repre
From playlist Lie groups
Lie Groups and Lie Algebras: Lesson 25 - the commutator and the Lie Algebra
Lie Groups and Lie Algebras: Lesson 25 - the commutator In this lecture we discover how to represent an infinitesimal commutator of the Lie group using a member of the Lie algebra. We promote the vector space spawned by the group generators to an algebra. Please consider supporting this
From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras: Lesson 18- Group Generators
Lie Groups and Lie Algebras: Lesson 18- Generators This is an important lecture! We work through the calculus of *group generators* and walk step-by-step through the exploitation of analyticity. That is, we use the Taylor expansion of the continuous functions associated with a Lie group o
From playlist Lie Groups and Lie Algebras
Louis-Clément-Lefevre: Representation varieties of fundamental groups of complex algebraic...
We study locally the representation varieties of fundamental groups of smooth complex algebraic varieties. These are schemes whose complex points parametrize such representations into linear algebraic groups. At a given representation, the structure of the formal local ring to the represen
From playlist Topology
Representation Theory(Repn Th) 3 by Gerhard Hiss
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Orbit of a set in abstract algebra
In this video we start to take a look at the orbit-stabilizer theorem. Our first stop is the orbit of a set. The orbit is created by taking an arbitrary element of a set and acting on that element by all the elements in the set of an an arbitrary group. In this video, we look at a few p
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
Introduction to Fiber Bundles part 2: Structure Groups
This is an important notion where we the transition functions of a certain fiber bundles lie in a smaller subgroup. This is important for setting up Streenrod's theorem.
From playlist Fiber bundles
Penghui Li Analytic atlas for stack of semistable bundles on elliptic curve and elliptic character s
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: Let G be a simply connected algebraic group, we define an analytic atlas of the moduli stack of semistable G-bundles on elliptic curves. Each chart in the
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
Gabriele NEBE - Lattices, Perfects lattices, Voronoi reduction theory, modular forms, ...
Lattices, Perfects lattices, Voronoi reduction theory, modular forms, computations of isometries and automorphisms The talks of Coulangeon will introduce the notion of perfect, eutactic and extreme lattices and the Voronoi's algorithm to enumerate perfect lattices (both Eulcidean and He
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Moonshine - 1 By Suresh Govindarajan
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Éric Gourgoulhon : Calcul tensoriel formel sur les variétés différentielles - Partie 2
Résumé : Le calcul tensoriel sur les variétés différentielles comprend l'arithmétique des champs tensoriels, le produit tensoriel, les contractions, la symétrisation et l'antisymétrisation, la dérivée de Lie le long d'un champ vectoriel, le transport par une application différentiable (pul
From playlist Mathematical Aspects of Computer Science
Representation Theory(Repn Th) 2 by Gerhard Hiss
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
The SL (2, R) action on spaces of differentials (Lecture 01) by Jayadev Athreya
DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o
From playlist Surface group representations and Projective Structures (2018)
Lie Groups and Lie Algebras: Lesson 22 - Lie Group Generators
Lie Groups and Lie Algebras: Lesson 22 - Lie Group Generators A Lie group can always be considered as a group of transformations because any group can transform itself! In this lecture we replace the "geometric space" with the Lie group itself to create a new collection of generators. P
From playlist Lie Groups and Lie Algebras
Stanford Seminar-Reconfiguring Sociomateriality
Paul Dourish University of California, Irvine This seminar series features dynamic professionals sharing their industry experience and cutting edge research within the human-computer interaction (HCI) field. Each week, a unique collection of technologists, artists, designers, and activist
From playlist Stanford Seminars
DDPS | Charting dynamics from data
In this DDPS talk from April 8, 2022, Daniel Floryan (University of Houston) presents recent work that fruitfully combines a classical idea from applied mathematics with modern methods of machine learning to learn minimal dynamical models directly from time series data. Description: We of
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
Lie Groups and Lie Algebras: Lesson 20 - Finite transformation example
Lie Groups and Lie Algebras: Lesson 20 - Finite transformation example A finite transformation is simply a lot of infinitesimal transformations! A Lie group, we have already show is a connected topological space and we know that any finite transformation can be built from a large product
From playlist Lie Groups and Lie Algebras