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
A short refresher on vectors. Before I introduce vector-based functions, it's important to look at vectors themselves and how they are represented in python™ and the IPython Notebook using SymPy.
From playlist Life Science Math: Vectors
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
Carolyn Yackel - Using Mathematics to Inform Fiber Arts Work - G4G14 Apr 2022
Using an example of itajime shibori the presenter will describe a project in which recognizing the role played by a mathematical concept limited the possible outcomes she could achieve and helped her to achieve all possible outcomes. Thereby she advocates the depth of mathematics that can
From playlist G4G14 Videos
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?
Multivariable Calculus | The notion of a vector and its length.
We define the notion of a vector as it relates to multivariable calculus and define its length. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Vectors for Multivariable Calculus
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
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
Vector Calculus 1: What Is a Vector?
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 Vector Calculus
AMMI Course "Geometric Deep Learning" - Lecture 10 (Gauges) - Taco Cohen
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July-August 2021 by Michael Bronstein (Imperial College/Twitter), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 10: Gauges • Gauge transformat
From playlist AMMI Geometric Deep Learning Course - First Edition (2021)
On Voevodsky's univalence principle - André Joyal
Vladimir Voevodsky Memorial Conference Topic: On Voevodsky's univalence principle Speaker: André Joyal Affiliation: Université du Québec á Montréal Date: September 11, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Univalent Foundations of Mathematics - Vladimir Voevodsky
Univalent Foundations of Mathematics - Vladimir Voevodsky Institute for Advanced Study December 10, 2010 The correspondence between homotopy types and higher categorical analogs of groupoids which was first conjectured by Alexander Grothendieck naturally leads to a view of mathematics wh
From playlist Mathematics
Affine Springer Fiber and Representation Theory of W algebra by Dan Xie
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)
Models from Biomathematics (Lecture 2) by Hari Shankar Mahato
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath Nandakumaran and Daniel Onofrei DATE: 26 August 2019 to 06 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Homogenization is a mathematical procedure to understa
From playlist Multi-scale Analysis And Theory Of Homogenization 2019
Michael Farber (2/24/22): Topological complexity of spherical bundles
I will start by describing the concept of a parametrized motion planning algorithm which allows to achieve high degree of flexibility and universality. The main part of the talk will focus on the problem of understanding the parametrized topological complexity of sphere bundles. I will exp
From playlist Topological Complexity Seminar
A Mathematical Theory of Solids-from Atomic to Macroscopic Scales - Weinan E
75th Anniversary Celebration School of Mathematics Weinan E Princeton University March 12, 2005 More videos on http://video.ias.edu
From playlist Mathematics
Dawid Kielak: Computing fibring of 3-manifoldsand free-by-cyclic groups
Abstract : We will discuss an analogy between the structure of fibrings of 3-manifolds and free-by-cyclic groups; we will focus on effective computability. This is joint work with Giles Gardam. Codes MSC : 20F65, 57K31, 20E36 Keywords : free-by-cyclic groups, fibering, Thurston norm, Thur
From playlist Virtual Conference
DDPS | The mathematical heart: a computational model for the simulation of the heart function
Mathematical models based on first principles can describe the interaction between electrical, mechanical and fluid-dynamical processes occurring in the heart, as well as the coupling with the external circulation. This is a classical multi-physics problem featuring multi-scale solutions i
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
6C Second equation for curvature on the blackboard
In this lecture I show you a second equation for curvature.
From playlist Life Science Math: Vectors