Introduction to Fiber Bundles Part 4: Torsor Interlude
Torsors and Principal Homogeneous Spaces. What is the difference?
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
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
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
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 the Principal Unit Normal Vector
Introduction to the Principal Unit Normal Vector
From playlist Calculus 3
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
Minhyong Kim: Recent progress on the effective Mordell problem
SMRI Algebra and Geometry Online: Minhyong Kim (University of Warwick) Abstract: In 1983, Gerd Faltings proved the Mordell conjecture stating that curves of genus at least two have only finitely many rational points. This can be understood as the statement that most polynomial equations
From playlist SMRI Algebra and Geometry Online
Index Theory, survey - Stephan Stolz [2018]
TaG survey series These are short series of lectures focusing on a topic in geometry and topology. May_8_2018 Stephan Stolz - Index Theory https://www3.nd.edu/~math/rtg/tag.html (audio fixed)
From playlist Mathematics
Equivariant principal bundles on toric varieties- Part 1 by Mainak Poddar
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
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"
Moduli Spaces of Principal 2-group Bundles and a Categorification of the Freed.. by Emily Cliff
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 Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Equivariant principal bundle over toric variety by Arijit Dey
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Jord Boeijink: On globally non-trivial almost-commutative manifolds
The framework of Connes' noncommutative geometry provides a generalisation of ordinary Riemannian spin manifolds to noncommutative manifolds. Within this framework, the special case of a (globally trivial) almost-commutative manifold has been shown to describe a (classical) gauge theory ov
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Branched Holomorphic Cartan Geometries by Sorin Dumitrescu
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
Introduction to Fiber Bundles Part 5.1: Steenrod's Theorem
This video is about how to reduce structure groups of fiber bundles.
From playlist Fiber bundles
Ana Balibanu: The partial compactification of the universal centralizer
Abstract: Let G be a semisimple algebraic group of adjoint type. The universal centralizer is the family of centralizers in G of regular elements in Lie(G), parametrized by their conjugacy classes. It has a natural symplectic structure, obtained by Hamiltonian reduction from the cotangent
From playlist Algebra
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