What is a Manifold? Lesson 12: Fiber Bundles - Formal Description
This is a long lesson, but it is not full of rigorous proofs, it is just a formal definition. Please let me know where the exposition is unclear. I din't quite get through the idea of the structure group of a fiber bundle fully, but I introduced it. The examples in the next lesson will h
From playlist What is a Manifold?
From playlist Drawing a sphere
Finding the volume and the surface area of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
Learn how to determine the volume of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
Find the volume of a sphere given the circumference
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
How do you find the surface area of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
What is a Manifold? Lesson 13: The tangent bundle - an illustration.
What is a Manifold? Lesson 13: The tangent bundle - an illustration. Here we have a close look at a complete example using the tangent bundle of the manifold S_1. Next lesson we look at the Mobius strip as a fiber bundle.
From playlist What is a Manifold?
algebraic geometry 21 Projective space bundles
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers projective space bundles, with Hirzebruch surfaces and scrolls as examples. It also includes a brief discussion of abstract varieties. Typo: in the definition o
From playlist Algebraic geometry I: Varieties
The TRUTH about TENSORS, Part 9: Vector Bundles
In this video we define vector bundles in full abstraction, of which tangent bundles are a special case.
From playlist The TRUTH about TENSORS
Michael Farber (2/24/22): Topological complexity of spherical bundles
I will start by describing the concept of a parametrized motion planning algorithm which allows to achieve high degree of flexibility and universality. The main part of the talk will focus on the problem of understanding the parametrized topological complexity of sphere bundles. I will exp
From playlist Topological Complexity Seminar
Commutative algebra 39 (Stably free modules)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We discuss the relation between stably free and free modules. We first give an example of a stably free module that is not fre
From playlist Commutative algebra
Even spaces and motivic resolutions - Michael Hopkins
Vladimir Voevodsky Memorial Conference Topic: Even spaces and motivic resolutions Speaker: Michael Hopkins Affiliation: Harvard University Date: September 13, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Caustics of Lagrangian homotopy spheres with stably trivial Gauss map - Daniel Alvarez-Gavela
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Caustics of Lagrangian homotopy spheres with stably trivial Gauss map Speaker: Daniel Alvarez-Gavela Date: May 14, 2021 For more video please visit https://www.ias.edu/video
From playlist Mathematics
Stable Homotopy Seminar, 3: The homotopy category of spectra
We discuss the Brown representability theorem, and give the Boardman-Vogt definition of the homotopy category of spectra. Examples include suspension spectra, Omega-spectra arising from cohomology theories, and Thom spectra. ~~~~~~~~~~~~~~~~======================~~~~~~~~~~~~~~~ This is
From playlist Stable Homotopy Seminar
Thomas Schick - Scalar curvature rigidity
Many manifolds are (positive) scalar curvature rigid: one can't increase the scalar curvature without shrinking the manifold. The first of these results was established by Llarull (for the round spheres), using spinorial techniques. We discuss the problem and the known solutions, including
From playlist Not Only Scalar Curvature Seminar
Mikhail Gromov - 3/4 Old, New and Unknown around Scalar Curvature
Geometry of scalar curvature, that is comparable in scope to symplectic geometry, mediates between two worlds: the domain of rigidity, one sees in convexity and the realm of softness, characteristic of topology, such as the cobordism theory. The aim of this course is threefold: 1. An ove
From playlist Mikhail Gromov - Old, New and Unknown around Scalar Curvature
Bernhard Hanke - Surgery, bordism and scalar curvature
One of the most influential results in scalar curvature geometry, due to Gromov-Lawson and Schoen-Yau, is the construction of metrics with positive scalar curvature by surgery. Combined with powerful tools from geometric topology, this has strong implications for the classification of suc
From playlist Not Only Scalar Curvature Seminar
Schemes 28: Examples of quasicoherent sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We give some examples of quasicoherent sheaves over affine schemes, and define vector bundles, line bundles, and the Picard group.
From playlist Algebraic geometry II: Schemes
How do you find the volume of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
