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
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
Definition of a Topological Space
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From playlist Topology
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
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
Topological Spaces: The Standard Topology on R^n
Today, we construct the standard topology, which gives us the way we usually think about R^n.
From playlist Topology & Manifolds
Topological Spaces: The Subspace Topology
Today, we discuss the subspace topology, which is a useful tool to construct new topologies.
From playlist Topology & Manifolds
Teena Gerhardt - 3/3 Algebraic K-theory and Trace Methods
Algebraic K-theory is an invariant of rings and ring spectra which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approac
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Topology 1.7 : More Examples of Topologies
In this video, I introduce important examples of topologies I didn't get the chance to get to. This includes The discrete and trivial topologies, subspace topology, the lower-bound and K topologies on the reals, the dictionary order, and the line with two origins. I also introduce (again)
From playlist Topology
What is a Manifold? Lesson 17 - Metric spaces (an aside)
What is a Manifold? Lesson 17 - An asisde on metric spaces
From playlist What is a Manifold?
Monica Vazirani: Representations of the affine BMW category
The BMW algebra is a deformation of the Brauer algebra, and has the Hecke algebra of type A as a quotient. Its specializations play a role in types B, C, D akin to that of the symmetric group in Schur-Weyl duality. I will discuss Walker’s TQFT-motivated 1-handle construction of a family of
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Finding the Interior, Exterior, and Boundary of a Set Topology
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From playlist Topology
Topology 1.6 : Metric Topology
In this video, I introduce the metric topology, and introduce how the topologies it generates align with the standard topologies on Euclidean space. Email : fematikaqna@gmail.com Subreddit : https://www.reddit.com/r/fematika Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Classical and Digital Topological Groups
A research talk presented at the Fairfield University Mathematics Research Seminar, October 6, 2022. Should be accessible to a general mathematics audience, combining ideas from topology, graph theory, and abstract algebra. The paper is by me and Dae Woong Lee, available here: https://arx
From playlist Research & conference talks
Matt Kahle (3/11/21): Configurations spaces of particles: homological solid, liquid, and gas
Title: Configurations spaces of particles: homological solid, liquid, and gas Abstract: Configuration spaces of points in the plane are well studied and the topology of such spaces is well understood. But what if you replace points by particles with some positive thickness, and put them i
From playlist Topological Complexity Seminar
Some digital topology and a Borsuk-Ulam Theorem
A talk about digital topology and a digital Borsuk-Ulam Theorem. I gave the talk in July 2015 at the Fairfield University Math REU program colloquium. The talk should be accessible to math undergraduates and enthusiasts, even better if you have some basic topology background. Link to my
From playlist Research & conference talks
Henry Adams - Bridging applied and geometric topology
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Henry Adams, Colorado State University Title: Bridging applied and geometric topology Abstract: I will advertise open questions in applied topology for which tools from geometric topology are relevant. If a point cloud is
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
Florian Frick (6/4/21): Rips complexes, projective codes, and zeros of odd maps
We will discuss a relation between the topology of Rips complexes (or their metric versions), the size of codes in projective spaces, and structural results for the zero set of odd maps from spheres to Euclidean space. On the one hand, this provides a new topological approach to problems i
From playlist Vietoris-Rips Seminar
Helmut Hofer Institute for Advanced Study April 5, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Topology: Interior, Exterior and Boundary
This video is about the interior, exterior, and boundary of sets.
From playlist Basics: Topology