Bundle map

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

The Map of Quantum Physics

This is the Map of Quantum Physics and quantum mechanics covering everything you need to know about this field in one image. Check out this video's sponsor https://brilliant.org/dos And grab this poster here: https://store.dftba.com/collections/domain-of-science/products/map-of-quantum-phy

From playlist The Map of Quantum Physics Expanded

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

What is a Manifold? Lesson 7: Differentiable Manifolds

From playlist What is a Manifold?

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

Schemes 47: Cotangent bundle

This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define the cotangent sheaf of a scheme, and calculate it for the projective line and then for general projective space.

From playlist Algebraic geometry II: Schemes

Manifolds #2: Charts

Today, we take a look at charts, their transition maps, and coordinate functions.

From playlist Manifolds

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

Modular spectral covers and Hecke eigensheaves on ... (Lecture 3) by Tony Pantev

Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries

From playlist Quantum Fields, Geometry and Representation Theory

Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 1) by Dror Varolin

PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo

From playlist Cauchy-Riemann Equations in Higher Dimensions 2019

Benson Farb, Part 2: Surface bundles, mapping class groups, moduli spaces, and cohomology

29th Workshop in Geometric Topology, Oregon State University, June 29, 2012

From playlist Benson Farb: 29th Workshop in Geometric Topology

Atiyah Duality by Samik Basu

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

Steven Bradlow - Exotic components of surface group representation varieties

Steven Bradlow Exotic components of surface group representation varieties, and their Higgs bundle avatars Moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. For representations into complex semisimple Lie groups,

From playlist Maryland Analysis and Geometry Atelier

Lachlan MacDonald, Chern-Weil theory for singular foliations

From playlist Global Noncommutative Geometry Seminar (Asia and Pacific)

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

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?

Geometry of the Global Nilpotent Cone (Lecture 2) by Ana Peon-Nieto

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)