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
Introduction to Fiber Bundles Part 3: Associated Bundles and Amalgamated Products
This is an incomplete introduction here. The basic idea is that the associated principal bundle knows all. This should be obvious since all bundles with G-structure are classified by H^1(X,G) --- it turns out you can recover your original bundle from a principal bundle by taking "amalgamat
From playlist Fiber bundles
More resources available at www.misterwootube.com
From playlist Measuring Basic Shapes
In this video, I define connectedness, which is a very important concept in topology and math in general. Essentially, it means that your space only consists of one piece, whereas disconnected spaces have two or more pieces. I also define the related notion of path-connectedness. Topology
From playlist Topology
How to find the area of a figure using multiple area's
👉 Learn how to find the area and perimeter of composite shapes. A composite shape is a shape that is composed of different shapes. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. To f
From playlist Area and Perimeter
How to find the composition of two areas by subtracting their areas
👉 Learn how to find the area and perimeter of composite shapes. A composite shape is a shape that is composed of different shapes. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. To f
From playlist Area and Perimeter
H. Guenancia - A decomposition theorem for singular spaces with trivial canonical class (Part 1)
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
Introduction to Fiber Bundles part 2: Structure Groups
This is an important notion where we the transition functions of a certain fiber bundles lie in a smaller subgroup. This is important for setting up Streenrod's theorem.
From playlist Fiber bundles
Takuro Mochizuki - Non-abelian Hodge Theory for Monopoles with Periodicity
Recently, we obtained equivalences between monopoles with periodicity and difference modules of various types, i.e., periodic monopoles and difference modules, doubly periodic monopoles and q-difference modules, and triply periodic monopoles and difference modules on elliptic curves. In th
From playlist Resurgence in Mathematics and Physics
H. Guenancia - A decomposition theorem for singular spaces with trivial canonical class (Part 2)
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
Quantization By Branes And Geometric Langlands Lecture 2 by Edward Witten
PROGRAM : QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS : Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Michel Brion: Homogeneous vector bundles over abelian varieties
Abstract: The objects of the talk are the translation-invariant vector bundles over an abelian variety. We will present a representation-theoretic description of these vector bundles, which displays a remarkable analogy with finite-dimensional representations of a compact connected Lie gro
From playlist Algebraic and Complex Geometry
Marcello Bernardara: Semiorthogonal decompositions and birational geometry of geometrically rational
Abstract:This is a joint work in progress with A. Auel. Let S be a geometrically rational del Pezzo surface over a field k. In this talk, I will show how the k-rationality of S is equivalent to the existence of some semiorthogonal decompositions of its derived category. In particular, the
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Elmar Schrohe: Fourier integral operators on manifolds with boundary and ...
Full Title: Fourier integral operators on manifolds with boundary and the Atiyah-Weinstein index theorem The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. (18.12.2014)
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Varieties with Trivial Canonical Class: discussion session - CIRM VIRTUAL EVENT
CIRM VIRTUAL EVENT Recorded during the meeting "Varieties with Trivial Canonical Class " the April 14, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Virtual Conference
Varieties with Trivial Canonical Class: problem session - CIRM VIRTUAL EVENT
CIRM VIRTUAL EVENT Recorded during the meeting "Varieties with Trivial Canonical Class " the April 16, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Virtual Conference
Learn how to find the composition area of a figure
👉 Learn how to find the area and perimeter of composite shapes. A composite shape is a shape that is composed of different shapes. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. To f
From playlist Area and Perimeter