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 16 - representations, connectedness, definition of Lie Group
Lie Groups and Lie Algebras: Lesson 16 - representations, connectedness, definition of Lie Group We cover a few concepts in this lecture: 1) we introduce the idea of a matrix representation using our super-simple example of a continuous group, 2) we discuss "connectedness" and explain tha
From playlist Lie Groups and Lie Algebras
In this clip I casually give a roundup of some of my current interests and also recommend you some literature. Get into Lie algebras, Lie groups and algebraic groups. Do it now! https://en.wikipedia.org/wiki/Lie_algebra http://www.jmilne.org/math/index.html
From playlist Algebra
Lie derivatives of differential forms
Introduces the lie derivative, and its action on differential forms. This is applied to symplectic geometry, with proof that the lie derivative of the symplectic form along a Hamiltonian vector field is zero. This is really an application of the wonderfully named "Cartan's magic formula"
From playlist Symplectic geometry and mechanics
Lie groups: Lie groups and Lie algebras
This lecture is part of an online graduate course on Lie groups. We discuss the relation between Lie groups and Lie algebras, and give several examples showing how they behave differently. Lie algebras turn out to correspond more closely to the simply connected Lie groups. We then explain
From playlist Lie groups
This lecture is part of an online graduate course on Lie groups. This lecture is about Lie's theorem, which implies that a complex solvable Lie algebra is isomorphic to a subalgebra of the upper triangular matrices. . For the other lectures in the course see https://www.youtube.com/playl
From playlist Lie groups
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
Lie Groups for Deep Learning w/ Graph Neural Networks
Lie Groups encode the symmetry of systems. We examine actions of a Lie group on a vector space, given their algebraic, topological and analysis based connectome. Deep Learning algorithms for Graph Neural Networks (GNN) are non trivial, and to understand them Lie Groups are essential! A r
From playlist Learn Graph Neural Networks: code, examples and theory
Edges that Lie on One Boundary of a Region in a Plane Graph | Graph Theory
Not all edges in a plane graph lie on the boundaries of two regions. If we draw a planar graph in the plane with no edge crossings, any edge that lies on a cycle will be on the boundaries of two regions, but edges that do not lie on cycles (bridges) will be on the boundary of only one regi
From playlist Graph Theory
Jean Michel BISMUT - Fokker-Planck Operators and the Center of the Enveloping Algebra
The heat equation method in index theory gives an explicit local formula for the index of a Dirac operator. Its Lagrangian counterpart involves supersymmetric path integrals. Similar methods can be developed to give a geometric formula for semi simple orbital integrals associated with the
From playlist Integrability, Anomalies and Quantum Field Theory
The Search for Siegel Zeros - Numberphile
Featuring Professor Tony Padilla. See https://brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) More links & stuff in full description below ↓↓↓ Yitang Zhang strikes again... Discrete mean estimates and the Landau-Siegel zero: https://arxiv.or
From playlist Tony Padilla on Numberphile
Moduli of p-divisible groups (Lecture 4) by Ehud De Shalit
PROGRAM PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France
From playlist Perfectoid Spaces 2019
Riddle For Genius - When Does The Thief Tell The Truth?
A funny thing happened in this logic video. I solved a harder problem than was presented! It works out to the same answer, and usually it's a good thing in math to solve a stronger theorem. But in education it can be confusing. So I will make a revised video! Update, see the revised video:
From playlist Logic Puzzles And Riddles
Kannan Soundararajan - Selberg's Contributions to the Theory of Riemann Zeta Function [2008]
http://www.ams.org/notices/200906/rtx090600692p-corrected.pdf January 11, 2008 3:00 PM Peter Goddard, Director Welcome Kannan Soundararajan Selberg's Contributions to the Theory of Riemann Zeta Function and Dirichlet L-Functions Atle Selberg Memorial Memorial Program in Honor of His
From playlist Number Theory
Proof: An Edge is a Bridge iff it Lies on No Cycles | Graph Theory
An edge of a graph is a bridge if and only if it lies on no cycles. We prove this characterization of graph bridges in today's graph theory lesson! My lesson on bridges: https://www.youtube.com/watch?v=zj_aFVuUATM Proof that a walk implies a path: https://www.youtube.com/watch?v=728bZWwT
From playlist Graph Theory
Logic Puzzles From The Tonight Show, 1982
Can you imagine a late night talk show featuring mathematical puzzles? Well back in 1982 the great Johnny Carson interviewed the great Raymond Smullyan, who shared a couple of fun logic puzzles. Can you solve them? Sources Raymond Smullyan on The Tonight Show Starring Johnny Carson https:
From playlist Math Puzzles, Riddles And Brain Teasers
Lie groups: Poincare-Birkhoff-Witt theorem
This lecture is part of an online graduate course on Lie groups. We state the Poincare-Birkhoff Witt theorem, which shows that the universal enveloping algebra (UEA) of a Lie algebra is the same size as a polynomial algebra. We prove it for Lie algebras of Lie groups and sketch a proof of
From playlist Lie groups