Structures on manifolds | Riemannian geometry | Differential geometry
In differential geometry, a G2 manifold is a seven-dimensional Riemannian manifold with holonomy group contained in G2. The group is one of the five exceptional simple Lie groups. It can be described as the automorphism group of the octonions, or equivalently, as a proper subgroup of special orthogonal group SO(7) that preserves a spinor in the eight-dimensional spinor representation or lastly as the subgroup of the general linear group GL(7) which preserves the non-degenerate 3-form , the associative form. The Hodge dual, is then a parallel 4-form, the coassociative form. These forms are calibrations in the sense of Reese Harvey and H. Blaine Lawson, and thus define special classes of 3- and 4-dimensional submanifolds. (Wikipedia).
Manifolds 1.3 : More Examples (Animation Included)
In this video, I introduce the manifolds of product manifolds, tori/the torus, real vectorspaces, matrices, and linear map spaces. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5koj5
From playlist Manifolds
Overview of gauge theory and submanifold geometry on G_2 manifolds - Simon Donaldson [2014]
Name: Simon Donaldson Event: Program: G2 manifolds Event URL: view webpage Title: Overview of gauge theory and submanifold geometry on G_2 manifolds, I Date: 2014-08-19 @3:30 PM
From playlist Mathematics
What is a Manifold? Lesson 6: Topological Manifolds
Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.
From playlist What is a Manifold?
I define topological manifolds. Motivated by the prospect of calculus on topological manifolds, I introduce smooth manifolds. At the end I point out how one needs to change the definitions, to obtain C^1 or even complex manifolds. To learn more about manifolds, see Lee's "Introduction to
From playlist Differential geometry
Manifolds 1.2 : Examples of Manifolds
In this video, I describe basic examples of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/IZO0G25
From playlist Manifolds
A review of the notes common to all formations of a G chord.
From playlist Music Lessons
Manifolds #5: Tangent Space (part 1)
Today, we introduce the notion of tangent vectors and the tangent vector space at a point on a manifold.
From playlist Manifolds
Orientations for Moduli Spaces in Higher-Dimensional Gauge Theory by Markus Upmeier
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
An Oxford Mathematics Graduate Supervision - Geometry and Physics in 7 Dimensions
So how do supervisor & graduate student work together? What happens in a graduate supervision? To find out, we filmed a supervision. Introducing Professor Jason Lotay & graduate student Izar Alonso Lorenzo as they discuss geometry in seven dimensions related to special holonomy, gauge the
From playlist Oxford Mathematics Student Tutorials and Graduate Supervisions
Lorenzo Foscolo: ALC manifolds with exceptional holonomy
We will describe the construction of complete non-compact Ricci-flat manifolds of dimension 7 and 8 with holonomy $G_{2}$ and Spin(7) respectively. The examples we consider all have non-maximal volume growth and an asymptotic geometry, so-called ALC geometry, that generalises to higher dim
From playlist Geometry
Exceptional holonomy and related geometric structures: Examples and moduli theory - Simon Donaldson
Marston Morse Lectures Topic: Exceptional holonomy and related geometric structures: Examples and moduli theory. Speaker: Simon Donaldson Affiliation: Stonybrook University Date: April 4, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Periodic Foams and Manifolds - Frank Lutz
Frank Lutz Technische Universitat Berlin March 2, 2011 WORKSHOP ON TOPOLOGY: IDENTIFYING ORDER IN COMPLEX SYSTEMS For more videos, visit http://video.ias.edu
From playlist Mathematics
Robert BRYANT - Algebraically Constrained Special Holonomy Metrics...
Robert BRYANT - Algebraically Constrained Special Holonomy Metrics and Second-order Associative 3-folds There are various methods known now for constructing more-or-less explicit metrics with special holonomy; most of these rely on assumptions of symmetry and/or reduction. Another promisi
From playlist Riemannian Geometry Past, Present and Future: an homage to Marcel Berger
Pre-recorded lecture 22: Open problems (part 2)
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Manifolds 1.1 : Basic Definitions
In this video, I give the basic intuition and definitions of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Manifolds
Exceptional holonomy and related geometric structures: Dimension reduction...- Simon Donaldson
Marston Morse Lectures Topic: Exceptional holonomy and related geometric structures: Dimension reduction and boundary value problems Speaker: Simon Donaldson Affiliation: Stonybrook University Date: April 6, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
What is a Manifold? Lesson 2: Elementary Definitions
This lesson covers the basic definitions used in topology to describe subsets of topological spaces.
From playlist What is a Manifold?
S. Donaldson - Boundary value problems for $G_2$ structures
In the lecture we consider the existence of G2 structures on 7-manifolds with boundary, with prescribed data on the boundary. In the first part we will review general background and theory, including Hitchin’s variational approach. We will then discuss in more detail reductions of the pr
From playlist Complex analytic and differential geometry - a conference in honor of Jean-Pierre Demailly - 6-9 juin 2017