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
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?
Visualization of tensors - part 1
This video visualizes tensors. It shows some introduction to tensor theory and demonstrates it with the Cauchy stress tensor. Future parts of this series will show more theory and more examples. It talks about the term 'tensor' as used in physics and math. In the field of AI the term 'te
From playlist Animated Physics Simulations
Linear Algebra 2q: Summary of Terms Encountered so Far
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications
What exactly is a vector? | Arithmetic and Geometry Math Foundations 30 | N J Wildberger
The notion of vector is here made completely explicit. Vectors arise in physics as forces, positions, velocities, accelerations, torques, displacements. It is useful to distinguish between points and vectors; they are different types of mathematical objects. In particular the position of a
From playlist Math Foundations
What is a vector? We gently introduce the i and j basis vectors and the idea of a column vector is presented. The algebra of addition, subtraction and scalar multiplication is discussed. Free ebook Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Take a sh
From playlist Introduction to Vectors
2 Construction of a Matrix-YouTube sharing.mov
This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.
From playlist Linear Algebra
Linear Algebra for Computer Scientists. 1. Introducing Vectors
This computer science video is one of a series on linear algebra for computer scientists. This video introduces the concept of a vector. A vector is essentially a list of numbers that can be represented with an array or a function. Vectors are used for data analysis in a wide range of f
From playlist Linear Algebra for Computer Scientists
Linear Algebra for Computer Scientists. 7. Linear Combinations of Vectors
This computer science video is one of a series on linear algebra for computer scientists. In this video you will learn about linear combinations of vectors, that is, you will learn how to create new vectors by scaling then adding other vectors together. You will also learn that some sets
From playlist Linear Algebra for Computer Scientists
Yonatan Harpaz - New perspectives in hermitian K-theory II
Warning: around 32:30 in the video, in the slide entitled "Karoubi's conjecture", a small mistake was made - in the third bulleted item the genuine quadratic structure appearing should be the genuine symmetric one (so both the green and red instances of the superscript gq should be gs), an
From playlist New perspectives on K- and L-theory
Yonatan Harpaz - New perspectives in hermitian K-theory III
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
Morphisms of Fibered Categories
The two category structure of fibered categories. We will need this for morphisms of Gerbes in the future.
From playlist Stacks
A categorical approach to representations in defining characteristic - Nate Harman
SL2 Seminar Topic: A categorical approach to representations in defining characteristic Speaker: Nate Harman Affiliation: Member, School of Mathematics Date: January 19, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Christoph Winges: Automorphisms of manifolds and the Farrell Jones conjectures
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Building on previous work of Bartels, Lück, Reich and others studying the algebraic K-theory and L-theory of discrete group rings, the validity of the Farrell-Jones Conjecture has be
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Ulrich Pennig: "Fell bundles, Dixmier-Douady theory and higher twists"
Actions of Tensor Categories on C*-algebras 2021 "Fell bundles, Dixmier-Douady theory and higher twists" Ulrich Pennig - Cardiff University, School of Mathematics Abstract: Classical Dixmier-Douady theory gives a full classification of C*-algebra bundles with compact operators as fibres
From playlist Actions of Tensor Categories on C*-algebras 2021
Partially wrapped Floer theory - Zach Sylvan
Workshop on Homological Mirror Symmetry: Methods and Structures Speaker:Zach Sylvan Title: Partially wrapped Floer theory Affilation: IAS Date: November 10, 2016 For more vide, visit http://video.ias.edu
From playlist Workshop on Homological Mirror Symmetry: Methods and Structures
Markus Land - L-Theory of rings via higher categories II
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
Clark Barwick - 3/3 Exodromy for ℓ-adic Sheaves
In joint work with Saul Glasman and Peter Haine, we proved that the derived ∞-category of constructible ℓ-adic sheaves ’is’ the ∞-category of continuous functors from an explicitly defined 1-category to the ∞-category of perfect complexes over ℚℓ. In this series of talks, I want to offer s
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Toronto Deep Learning Series, 11-Feb-2019 https://tdls.a-i.science/events/2019-02-11 TENSOR FIELD NETWORKS: ROTATION- AND TRANSLATION-EQUIVARIANT NEURAL NETWORKS FOR 3D POINT CLOUDS We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, a
From playlist Math and Foundations