Topology (What is a Topology?)
What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b
From playlist Topology
Definition of a Topological Space
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From playlist Topology
Algebraic Topology - 5.1 - Mappings Spaces and the Compact Open Topology
We define the compact open topology on mapping spaces.
From playlist Algebraic Topology
Topology 1.1 : Open Sets of Reals
In this video, I give a definition of the open sets on the real numbers. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
I define closed sets, an important notion in topology and analysis. It is defined in terms of limit points, and has a priori nothing to do with open sets. Yet I show the important result that a set is closed if and only if its complement is open. More topology videos can be found on my pla
From playlist Topology
Manifolds 2.3 : Smooth Maps and Diffeomorphisms
In this video, I introduce examples and properties of smooth maps, and show the invariance theorems for diffeomorphisms. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet Playlist :
From playlist Manifolds
Topology 1.4 : Product Topology Introduction
In this video, I define the product topology, and introduce the general cartesian product. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Manifolds 2.2 : Examples and the Smooth Manifold Chart Lemma
In this video, I introduce examples of smooth manifolds, such as spheres, graphs of smooth functions, real vectorspaces, linear map spaces, and the Grassmannian of real vectorspaces (G_k(V)). Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet Play
From playlist Manifolds
Topology 1.3 : Basis for a Topology
In this video, I define what a basis for a topology is. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
This lecture was held by Abel Laureate John Milnor at The University of Oslo, May 25, 2011 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2011 1. "Spheres" by Abel Laureate John Milnor, Institute for Mathematical
From playlist Abel Lectures
Introduction to Complex Differential Geometry -- Lecture 1 -- Intuition and Definition of Manifolds
I recently completed my Ph.D. under the supervision of Ben Andrews at the Australian National University and Gang Tian at Beijing and Princeton University. My Ph.D. thesis was in the subject of complex differential geometry, the interplay between complex analysis, algebraic geometry, and d
From playlist Research Lectures
Hengrui Luo (4/22/20): Lower dimensional topological information: Theory and applications
Title: Lower dimensional topological information: Theory and applications Abstract: Topological data analysis (TDA) allows us to explore the topological features of a dataset. Among topological features, lower dimensional ones are of growing interest in mathematics and statistics due to t
From playlist AATRN 2020
A1-algebraic topology : genesis, youth and beyond - Fabien Morel
Vladimir Voevodsky Memorial Conference Topic: A1-algebraic topology : genesis, youth and beyond Speaker: Fabien Morel Affiliation: Mathematisches Instit der Universität München Date: September 11, 2018 For more video please visit http://video.ias.edu
From playlist Vladimir Voevodsky Memorial Conference
I define topological manifolds. Motivated by the prospect of calculus on topological manifolds, I introduce smooth manifolds. At the end I point out how one needs to change the definitions, to obtain C^1 or even complex manifolds. To learn more about manifolds, see Lee's "Introduction to
From playlist Differential geometry
Constructions in symplectic and contact topology via h-principles - Oleg Lazarev
More videos on http://video.ias.edu
From playlist Mathematics
Prerequisites III: Manifolds & Fiber Bundles - Maurice Weiler
Video recording of the First Italian Summer School on Geometric Deep Learning, which took place in July 2022 in Pescara. Slides: https://www.sci.unich.it/geodeep2022/slides/Manifolds_and_Fiber_Bundles.pdf
From playlist First Italian School on Geometric Deep Learning - Pescara 2022
Invariants of 4-manifolds - Tye Lidman
Short Talks by Postdoctoral Members Tye Lidman - September 24, 2015 http://www.math.ias.edu/calendar/event/88224/1443125700/1443126600 More videos on http://video.ias.edu
From playlist Short Talks by Postdoctoral Members
Finding the Interior, Exterior, and Boundary of a Set Topology
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From playlist Topology