We introduce an important class of spaces called cell complexes or CW complexes, focusing on examples.
From playlist Algebraic Topology
The projective Quadruple quad formula | Rational Geometry Math Foundations 148 | NJ Wildberger
In this video we introduce the projective version of the Quadruple quad formula, which not only controls the relationship between four projective points, but has a surprising connection with the geometry of the cyclic quadrilateral. The projective quadruple quad function is called R(a,b,
From playlist Math Foundations
Complete Derivation: Universal Property of the Tensor Product
Previous tensor product video: https://youtu.be/KnSZBjnd_74 The universal property of the tensor product is one of the most important tools for handling tensor products. It gives us a way to define functions on the tensor product using bilinear maps. However, the statement of the universa
From playlist Tensor Products
What is a linear combination of your unit vectors
http://www.freemathvideos.com In this video series I will show you how to find the unit vector when given a vector in component form and as a linear combination. A unit vector is simply a vector with the same direction but with a magnitude of 1 and an initial point at the origin. It is i
From playlist Vectors - Understanding
Calculus 3: Tensors (1 of 28) What is a Tensor?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a tensor. A tensor is a mathematical representation of a scalar (tensor of rank 0), a vector (tensor of rank 1), a dyad (tensor of rank 2), a triad (tensor or rank 3). Next video in t
From playlist CALCULUS 3 CH 10 TENSORS
What is a Tensor? Lesson 11: The metric tensor
What is a Tensor 11: The Metric Tensor
From playlist What is a Tensor?
Special Topics - GPS (1 of 100) The GPS Constellation
Visit http://ilectureonline.com for more math and science lectures! In this video I will overview the content of the GPS (Global Positioning System) and explain the GPS constellation. Next video in this series can be seen at: https://youtu.be/Cwr6oLdWvJQ
From playlist SPECIAL TOPICS 2 - GPS
Henry Adams and Enrique Alvarado: An introduction to Morse theory
We give an introduction to Morse theory. Given a space equipped with a real-valued function, one can use Morse theory to produce a compact cellular model for that space. Furthermore, the cellular model reflects important properties of the function. We describe CW cell complexes, the Morse
From playlist Tutorials
Graham ELLIS - Computational group theory, cohomology of groups and topological methods 1
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Graham ELLIS - Computational group theory, cohomology of groups and topological methods 3
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Stable Homotopy Seminar, 2: Fiber and Cofiber Sequences
We review some unstable homotopy theory, especially the construction of fiber and cofiber sequences of spaces, and how they induce long exact sequences on homotopy and homology/cohomology. (There's a mistake pointed out by Jeff Carlson: when I take a CW-approximation at one point, I have
From playlist Stable Homotopy Seminar
Basic Homotopy Theory 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)
Homological Algebra(Homo Alg 1) by Graham Ellis
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Stable Homotopy Seminar, 3: The homotopy category of spectra
We discuss the Brown representability theorem, and give the Boardman-Vogt definition of the homotopy category of spectra. Examples include suspension spectra, Omega-spectra arising from cohomology theories, and Thom spectra. ~~~~~~~~~~~~~~~~======================~~~~~~~~~~~~~~~ This is
From playlist Stable Homotopy Seminar
Sucharit Sarkar - Khovanov homotopy type
June 29, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry
From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry II
Discrete Morse Theory 2.0 [Ximena Fernández]
Is there any way to understand the homotopy type of CW-complexes from its combinatorial structure? In this tutorial we explain the main ideas behind discrete Morse theory, and present a refinement of the theory that allows to answer positively the previous question. We apply these results
From playlist Tutorial-a-thon 2021 Fall
Homological Algebra(Homo Alg) 5 by Graham Ellis
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Calculus 3: Tensors (10 of 45) Tensor of Rank 3: The Triad
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain a triad tensor “matrix”. A triad is a tensor of rank 3 has 27 components in a row, column, and page 3 dimensional “matrix”; and each component will have 3 subscripts. Next video in the series
From playlist CALCULUS 3 CH 10 TENSORS
Graham ELLIS - Computational group theory, cohomology of groups and topological methods 2
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory