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?
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
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
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
This knot is very useful for adjusting tie downs quickly and easily. For example, a tarp could be held down by a series of these knots and be made very tight so the wind cannot make it rise, and easily be removed simply by sliding the knots later. A taut line knot is also used to keep larg
From playlist Practical Projects & Skills
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?
The TRUTH about TENSORS, Part 10: Frames
What do the octonions have to do with spheres? Skip to the end of the video to find out!
From playlist The TRUTH about TENSORS
Introduction to Fiber Bundles Part 4: Torsor Interlude
Torsors and Principal Homogeneous Spaces. What is the difference?
From playlist Fiber bundles
A. Höring - A decomposition theorem for singular spaces with trivial canonical class (Part 3)
The Beauville-Bogomolov decomposition theorem asserts that any compact Kähler manifold with numerically trivial canonical bundle admits an étale cover that decomposes into a product of a torus, an irreducible, simply-connected Calabi-Yau, and holomorphic symplectic manifolds. With the deve
From playlist Ecole d'été 2019 - Foliations and algebraic geometry
The TRUTH about TENSORS, Part 8: Tangent bundles & vector fields
In this video, we discuss the definition of the tangent bundle of a manifold, which in turns inspires the more general definition of vector bundles, to be discussed in the next video. The notion of tangent bundle, further lets us formalize our intuitive notion of vector fields.
From playlist The TRUTH about TENSORS
Noah Arbesfeld: A geometric R-matrix for the Hilbert scheme of points on a general surface
Abstract: We explain how to use a Virasoro algebra to construct a solution to the Yang-Baxter equation acting in the tensor square of the cohomology of the Hilbert scheme of points on a generalsurface S. In the special case where the surface S is C2, the construction appears in work of Mau
From playlist Algebraic and Complex Geometry
Charles Rezk: Elliptic cohomology and elliptic curves (Part 4)
The lecture was held within the framework of the Felix Klein Lectures at Hausdorff Center for Mathematics on the 10. June 2015
From playlist HIM Lectures 2015
Alina Marian - On the tautological cohomology of the moduli space of curves
Worldwide Center of Mathematics. Research lecture
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Alessandro Giacchetto - The Negative Side of Witten’s Conjecture
In 2017, Norbury introduced a collection of cohomology classes on the moduli space of curves, and predicted that their intersection with psi classes solves the KdV hierarchy. In a joint work in progress with N. Chidambaram and E. Garcia-Failde, we consider a deformation of Norbury’s class
From playlist Workshop on Quantum Geometry
Vladimiro Benedetti: Orbital degeneracy loci
Abstract: I will present a joint work with Sara Angela Filippini, Laurent Manivel and Fabio Tanturri (arXiv: 1704.01436). We introduce a new class of varieties, called orbital degeneracy loci. The idea is to use any orbit closure in a representation of an algebraic group to generalise the
From playlist Algebraic and Complex Geometry
Session 2 - Aspects of 2d (0,2) theories: Abhijit Gadde
https://strings2015.icts.res.in/talkTitles.php
From playlist Strings 2015 conference
Andrei Negut: Hilbert schemes of K3 surfaces
Abstract: We give a geometric representation theory proof of a mild version of the Beauville-Voisin Conjecture for Hilbert schemes of K3 surfaces, namely the injectivity of the cycle map restricted to the subring of Chow generated by tautological classes. Although other geometric proofs o
From playlist Algebraic and Complex Geometry
Algebraic Topology - 12.2 - Fiber Bundles
From playlist Algebraic Topology
S. Diverio - Kobayashi hyperbolicity of complex projective manifolds and foliations (Part 3)
The aim of this mini course is to highlight some links between the study of the Kobayashi hyperbolicity properties of complex projective manifolds and holomorphic foliations. A compact complex space is Kobayashi hyperbolic if and only if every holomorphic map from the complex plane to it
From playlist Ecole d'été 2019 - Foliations and algebraic geometry