Homotopy theory | Homological algebra
In mathematics, a topological half-exact functor F is a functor from a fixed topological category (for example CW complexes or pointed spaces) to an abelian category (most frequently in applications, category of abelian groups or category of modules over a fixed ring) that has a following property: for each sequence of spaces, of the form: X → Y → C(f) where C(f) denotes a mapping cone, the sequence: F(X) → F(Y) → F(C(f)) is exact. If F is a contravariant functor, it is half-exact if for each sequence of spaces as above,the sequence F(C(f)) → F(Y) → F(X) is exact. Homology is an example of a half-exact functor, andcohomology (and generalized cohomology theories) are examples of contravariant half-exact functors.If B is any fibrant topological space, the (representable) functor F(X)=[X,B] is half-exact. (Wikipedia).
Illustrates the solution of an exact first-order differential equation. Free books: http://bookboon.com/en/differential-equations-with-youtube-examples-ebook http://www.math.ust.hk/~machas/differential-equations.pdf
From playlist Differential Equations with YouTube Examples
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
A Group Theoretic Description | The Geometry of SL(2,Z), Section 2.1
Expressing the complex upper half plane as a quotient of topological (in fact, Lie) groups. Twitter: https://twitter.com/KristapsBalodi3 Topological Groups (0:00) A Lemma on Stabilization (7:19) Connecting Geometry and Algebra (9:55)
From playlist The Geometry of SL(2,Z)
Exact Differential Equations - Intro
Updated version available! https://youtu.be/qpPoI9gFF0g
From playlist Mathematical Physics I Youtube
Differential Equations: Exact DEs Example 1
It's important to be able to classify a differential equation so we can pick the right method to solve it. In this video, I run through the steps of how to classify a first order differential equation as separable, linear, exact, or neither.
From playlist Differential Equations
Categories 5 Limits and colimits
This lecture is part of an online course on category theory. We define limits and colimits of functors, and show how various constructions (products, kernels, inverse limits, and so on) are special cases of this. We also describe how adoint functors preserve limits or colimits. For the
From playlist Categories for the idle mathematician
This video is about metric spaces and some of their basic properties.
From playlist Basics: Topology
The big mathematics divide: between "exact" and "approximate" | Sociology and Pure Maths | NJW
Modern pure mathematics suffers from a major schism that largely goes unacknowledged: that many aspects of the subject are parading as "exact theories" when in fact they are really only "approximate theories". In this sense they can be viewed either as belonging more properly to applied ma
From playlist Sociology and Pure Mathematics
Differential Equations: Exact DEs Introduction 2
In part two of the introduction to exact differential equations, we explore how exactness makes solving exact differential equations easier. We then lay down the theory of how to actually solve them.
From playlist Differential Equations
Ryan Reich - On Beilinson's "How to glue perverse sheaves"
Research lecture at the Worldwide Center of Mathematics
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Grothendieck-Serre Duality by Suresh Nayak
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)
Paul Turner: A hitchhiker's guide to Khovanov homology - Part I
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 Geometry
Purity, the Gysin sequence, cohomology of projective space, elementary fibrations, statement of Artin comparison
From playlist Étale cohomology and the Weil conjectures
Stable 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)
Étale cohomology 9/10/2020 Part 2
Čech cohomology
From playlist Étale cohomology and the Weil conjectures
Charles Rezk - 4/4 Higher Topos Theory
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/RezkNotesToposesOnlinePart4.pdf In this series of lectures I will give an introduction to the concept of "infinity
From playlist Toposes online
Moduli of p-divisible groups (Lecture 1) by Ehud De Shalit
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
What is a Manifold? Lesson 2: Elementary Definitions
This lesson covers the basic definitions used in topology to describe subsets of topological spaces.
From playlist What is a Manifold?