Geometric Algebra - Rotors and Quaternions
In this video, we will take note of the even subalgebra of G(3), see that it is isomorphic to the quaternions and, in particular, the set of rotors, themselves in the even subalgebra, correspond to the set of unit quaternions. This brings the entire subject of quaternions under the heading
From playlist Math
Isometry groups of the projective line (I) | Rational Geometry Math Foundations 138 | NJ Wildberger
The projective line can be given a Euclidean structure, just as the affine line can, but it is a bit more complicated. The algebraic structure of this projective line supports some symmetries. Symmetry in mathematics is often most efficiently encoded with the idea of a group--a technical t
From playlist Math Foundations
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
Introduction to Fiber Bundles part 1: Definitions
We give the definition of a fiber bundle with fiber F, trivializations and transition maps. This is a really basic stuff that we use a lot. Here are the topics this sets up: *Associated Bundles/Principal Bundles *Reductions of Structure Groups *Steenrod's Theorem *Torsor structure on arith
From playlist Fiber bundles
A panoramic view of Mathematics Research @ICTS by Varun Thakre and Anish Mallick
ICTS In-house 2019 Organizers: Adhip Agarwala, Ganga Prasath, Rahul Kashyap, Gayathri Raman, Priyanka Maity Date and Time: 23rd April, 2019 Venue: Ramanujan Lecture Hall, ICTS Bangalore inhouse@icts.res.in An exclusive day to exchange ideas and discuss research amongst members of ICTS.
From playlist ICTS In-house 2019
Symplectic topology and the loop space - Jingyu Zhao
Topic: Symplectic topology and the loop space Speaker: Jingyu Zhao, Member, School of Mathematics Time/Room: 4:45pm - 5:00pm/S-101 More videos on http://video.ias.edu
From playlist Mathematics
Exploring Symplectic Embeddings and Symplectic Capacities
Speakers o Alex Gajewski o Eli Goldin o Jakwanul Safin o Junhui Zhang Project Leader: Kyler Siegel Abstract: Given a domain (e.g. a ball) in Euclidean space, we can ask what is its volume. We can also ask when one domain can be embedded into another one without distorting volumes. These
From playlist 2019 Summer REU Presentations
Symplectic embeddings, integrable systems and billiards - Vinicius Ramos
Symplectic Dynamics/Geometry Seminar Topic: Symplectic embeddings, integrable systems and billiards Speaker: Vinicius Ramos Affiliation: Member, School of Mathematics Date: January 27, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Jean-Pierre Bourguignon: Revisiting the question of dependence of spinor fields and Dirac [...]
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 Geometry
Harold Steinacker - Covariant Cosmological Quantum Space-Time
Covariant Cosmological Quantum Space-Time: Higher-spin and Gravity in the IKKT Matrix Model https://indico.math.cnrs.fr/event/4272/attachments/2260/2717/IHESConference_Harold_STEINACKER.pdf
From playlist Space Time Matrices
Spinors and the Clutching Construction
What’s the connection between spinors and the clutching construction? Chapters: 00:00 Why should we care? 00:32 Spinors in pop culture 01:34 Graph 03:15 Wall 03:42 Tome 04:18 Sir Roger Penrose 04:53 Hopf fibration 06:23 Paul Dirac 07:12 The belt trick 08:54 Exterior derivative 09:49 Deter
From playlist Summer of Math Exposition Youtube Videos
Rudolf Zeidler - Scalar and mean curvature comparison via the Dirac operator
I will explain a spinorial approach towards a comparison and rigidity principle involving scalar and mean curvature for certain warped products over intervals. This is motivated by recent scalar curvature comparison questions of Gromov, in particular distance estimates under lower scalar c
From playlist Talks of Mathematics Münster's reseachers
Flexibility in symplectic and contact geometry – Emmy Murphy – ICM2018
Geometry | Topology Invited Lecture 5.6 | 6.2 Flexibility in symplectic and contact geometry Emmy Murphy Abstract: Symplectic and contact structures are geometric structures on manifolds, with relationships to algebraic geometry, geometric topology, and mathematical physics. We discuss a
From playlist Geometry
Symplectic geometry of surface group representations - William Goldman
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Symplectic geometry of surface group representations Speaker: William Goldman Affiliation: Member, School of Mathematics Date: February 28, 2022 If G is a Lie group whose adjoint representation preserves a nondegenerate sy
From playlist Mathematics
Sir Michael Atiyah, What is a Spinor ?
Sir Michael Atiyah, University of Edinburgh What is a Spinor?
From playlist Conférence en l'honneur de Jean-Pierre Bourguignon
Recording during the meeting "Twistors and Loops Meeting in Marseille" the September 02, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisua
From playlist Mathematical Physics
Brent Pym: Holomorphic Poisson structures - lecture 3
The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a cano
From playlist Virtual Conference
16/11/2015 - Roger Penrose - Palatial Twistor Theory: a Quantum Approach to Classical Space-Time
https://philippelefloch.files.wordpress.com/2015/11/2015-ihp-rogerpenrose.pdf Abstract. Up until recently, the applications of twistor theory to general relativity have been rather limited, applicable mainly to special solutions of the Einstein equations and to complex solutions which are
From playlist 2015-T3 - Mathematical general relativity - CEB Trimester
The Lie-algebra of Quaternion algebras and their Lie-subalgebras
In this video we discuss the Lie-algebras of general quaternion algebras over general fields, especially as the Lie-algebra is naturally given for 2x2 representations. The video follows a longer video I previously did on quaternions, but this time I focus on the Lie-algebra operation. I st
From playlist Algebra