An Introduction to Algebraic Geometry : Chapter 1, Section 1 - Affine Varieties
Channel: xdd1
Date: 2022-08-16

This is the first part of my playlist going over the content in Robin Hartshorne's book Algebraic Geometry - in this part we go over section one (affine varieties) of chapter one (varieties), covering the visualization of zero-sets of polynomials, the Zariski Topology generated by zero sets, the ideal of subsets of affine space, the relation between ideals and zero sets, affine varieties, properties of Noetherian Topological Spaces, basic dimension theory of varieties, and end off with the unofficial concept of potential irreducible to motivate quasi-affine varieties.

The collection of links this lecture is as follows :

https://docs.google.com/document/d/1I2ImYKkun7Rhi21TsPmQWHKnWYnXBGB5NbfbzSFphdY/edit?usp=sharing - Video Script
https://docs.google.com/presentation/d/1U5MQmK9Q-kPGKfN5iIc-rAOih3m19vD6VHHR2gTLIEM/edit?usp=sharing - Slides
http://abstract.ups.edu/download.html - Abstract Algebra, Theory and applications (Tom Judson)
https://www.math.ru.nl/~mueger/topology.pdf - Topology for the Working Mathematician (Michael Müger)
http://www.cs.cmu.edu/~kmcrane/Projects/ModelRepository/ - Link to Blender Library with Topology Cow
https://musescore.com/user/21974371/scores/4220336 - Nickolas Kaedalus' arrangement of Mass Destruction from Persona 3
https://www.youtube.com/c/OliverLugg - Oliver Lugg's channel, go learn category theory there if you haven't already


Chapters :

00:00-02:00 : Introduction 
02:00-02:58 : Preliminaries
02:58-05:45 : Shapes from Zeroes
05:45-13:10 : The Topology of Zeroes
13:10-23:08 : Topology ↔ Algebra
23:08-25:50 : Noetherian, Topologically
25:50-33:30 : The Part with Dimension Theory
33:30-37:40 : Moving Beyond the Affine
37:40 : End(ing Remarks)