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
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?
Algebraic Topology - 12.2 - Fiber Bundles
From playlist Algebraic Topology
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 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
What is a Tensor? Lesson 11: The metric tensor
What is a Tensor 11: The Metric Tensor
From playlist What is a Tensor?
Introduction to Fiber Bundles Part 4: Torsor Interlude
Torsors and Principal Homogeneous Spaces. What is the difference?
From playlist Fiber bundles
Schemes 48: The canonical sheaf
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we define the canonical sheaf, giev a survey of some applications (Riemann-Roch theorem, Serre duality, canonical embeddings, Kodaira dimensio
From playlist Algebraic geometry II: Schemes
Caucher Birkar's Fields Medal Laudatio — Christopher Hacon — ICM2018
The work of Caucher Birkar Christopher Hacon ICM 2018 - International Congress of Mathematicians © www.icm2018.org Os direitos sobre todo o material deste canal pertencem ao Instituto de Matemática Pura e Aplicada, sendo vedada a utilização total ou parcial do conteúdo sem autorização
From playlist Special / Prizes Lectures
Enrica Floris: Invariance of plurigenera for foliations on surfaces
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex 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
R. Lazarsfeld: The Equations Defining Projective Varieties part 4
The lecture was held within the framework of the Junior Hausdorff Trimester Program Algebraic Geometry. (6.-22.1.2014)
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
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
Nigel Hitchin "Higgs bundles, past and present" [2012]
2012 FIELDS MEDAL SYMPOSIUM Thursday, October 18 Geometric Langlands Program and Mathematical Physics Nigel Hitchin, Oxford University Higgs bundles, past and present The talk will be an overview of the moduli spaces of Higgs bundles, or equivalently solutions to the so-called Hitchin eq
From playlist Number Theory
Differential geometry of the Torelli map (Lecture 5) by Alessandro Ghigi and Paola Frediani
DISCUSSION MEETING TOPICS IN HODGE THEORY (HYBRID) ORGANIZERS: Indranil Biswas (TIFR, Mumbai, India) and Mahan Mj (TIFR, Mumbai, India) DATE: 20 February 2023 to 25 February 2023 VENUE: Ramanujan Lecture Hall and Online This is a followup discussion meeting on complex and algebraic ge
From playlist Topics in Hodge Theory - 2023
Projectivity of the moduli space of KSBA stable pairs and applications - Zsolt Patakfalvi
Zsolt Patakfalvi Princeton University February 24, 2015 KSBA (Kollár-Shepherd-Barron-Alexeev) stable pairs are higher dimensional generalizations of (weighted) stable pointed curves. I will present a joint work in progress with Sándor Kovács on proving the projectivity of this moduli spac
From playlist Mathematics
Positivity and algebraic integrability of holomorphic foliations – Carolina Araujo – ICM2018
Algebraic and Complex Geometry Invited Lecture 4.7 Positivity and algebraic integrability of holomorphic foliations Carolina Araujo Abstract: The theory of holomorphic foliations has its origins in the study of differential equations on the complex plane, and has turned into a powerful t
From playlist Algebraic & Complex Geometry