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
Algebraic topology: Introduction
This lecture is part of an online course on algebraic topology. This is an introductory lecture, where we give a quick overview of some of the invariants of algebraic topology (homotopy groups, homology groups, K theory, and cobordism). The book "algebraic topology" by Allen Hatcher men
From playlist Algebraic topology
AlgTopReview: An informal introduction to abstract algebra
This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is
From playlist Algebraic Topology
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
In this video, I introduce the order topology and prove that it is Hausdorff. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist 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
AlgTop1: One-dimensional objects
This is the first lecture of this beginner's course in Algebraic Topology (after the Introduction). In it we introduce the two basic one-dimensional objects: the line and circle. The latter has quite a few different manifestations: as a usual Euclidean circle, as the projective line of one
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Fields Medal Lecture: Cohomology of arithmetic groups — Akshay Venkatesh — ICM2018
Cohomology of arithmetic groups Akshay Venkatesh Abstract: The topology of “arithmetic manifolds”, such as the space of lattices in Rn modulo rotations, encodes subtle arithmetic features of algebraic varieties. In some cases, this can be explained because the arithmetic manifold itself c
From playlist Special / Prizes Lectures
Jens Hemelaer: Toposes in arithmetic noncommutative geometry
Talk by Jens Hemelaer in Global Noncommutative Geometry Seminar (Americas) on February 5, 2021
From playlist Global Noncommutative Geometry Seminar (Americas)
Set Theory: Types of Sets, Unions and Intersections
We've already learned a little bit about set theory when we first started using interval notation. Let's expand on this a little bit to include sets that merely list some elements, so that we can understand how to find the union and intersection of two sets. This is good notation to know r
From playlist Algebra 1 & 2
Fun with finite covers of 3-manifolds - Nathan Dunfield
https://www.math.ias.edu/seminars/abstract?event=47565
From playlist Members Seminar
Jens Hemelaer - Toposes of presheaves on monoids as generalized topological spaces
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/HemelaerSlidesToposesOnline.pdf Various ideas from topology have been generalized to toposes, for example surjection
From playlist Toposes online
Nathan Dunfield, Lecture 1: Fun with Finite Covers of 3-Manifolds
33rd Workshop in Geometric Topology, Colorado College, June 9, 2016
From playlist Nathan Dunfield: 33rd Workshop in Geometric Topology
Alexander Petrov - Representations of Galois groups and families of algebraic varieties
Alexander Petrov (MPIM) One of the central methods of arithmetic geometry is the study of algebraic varieties through the action of the Galois group on topological invariants of varieties such as cohomology and homotopy groups. An important question in this area is the problem of classifi
From playlist Azat Miftakhov Days Against the War
Analysis and topology on locally symmetric spaces - Akshay Venkatesh
Members' Seminar Topic: Analysis and topology on locally symmetric spaces Speaker: Akshay Venkatesh Affiliation: Stanford University; Distinguished Visiting Professor, School of Mathematics Date: October 9, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Peter Sarnak - Nodal domains of eigenmodes of the Laplacian and of random functions [2013]
Gelfand Centennial Conference: A View of 21st Century Mathematics MIT, Room 34-101, August 28 - September 2, 2013 Peter Sarnak Saturday, August 31 10:50AM Nodal domains of eigenmodes of the Laplacian and of random functions Abstract: It is believed that the eigenfunctions of the quantiz
From playlist Number Theory
Grothendieck Pairs and Profinite Rigidity - Martin Bridson
Arithmetic Groups Topic: Grothendieck Pairs and Profinite Rigidity Speaker: Martin Bridson Affiliation: Oxford University Date: January 26, 2022 If a monomorphism of abstract groups H↪G induces an isomorphism of profinite completions, then (G,H) is called a Grothendieck pair, recalling t
From playlist Mathematics
The rising sea: Grothendieck on simplicity and generality - Colin McLarty [2003]
Slides for this talk: https://drive.google.com/file/d/1yDmqhdcKo6-YpDpRdHh2hvuNirZVbcKr/view?usp=sharing Notes for this talk: https://drive.google.com/open?id=1p45B3Hh8WPRhdhQAd0Wq0MvmY0JYSnmc The History of Algebra in the Nineteenth and Twentieth Centuries April 21 - 25, 2003 Colin Mc
From playlist Mathematics
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