The circle and projective homogeneous coordinates | Universal Hyperbolic Geometry 7a | NJ Wildberger
Universal hyperbolic geometry is based on projective geometry. This video introduces this important subject, which these days is sadly absent from most undergrad/college curriculums. We adopt the 19th century view of a projective space as the space of one-dimensional subspaces of an affine
From playlist Universal Hyperbolic Geometry
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
The circle and projective homogeneous coordinates (cont.) | Universal Hyperbolic Geometry 7b
Universal hyperbolic geometry is based on projective geometry. This video introduces this important subject, which these days is sadly absent from most undergrad/college curriculums. We adopt the 19th century view of a projective space as the space of one-dimensional subspaces of an affine
From playlist Universal Hyperbolic Geometry
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
What is a Vector Space? Definition of a Vector space.
From playlist Linear Algebra
WHEN SPACE DOES NOT HAVE DISTANCE: What is the Long Line in Math and Other Examples (Version 2.0)
In many ways metric spaces grant a large amount of structure to a topological space. So it's natural to ask what happens when space does not have distance defined on it. Can we still talk about things like size or even compare these types of spaces to other metrizable spaces? The answer is
From playlist The New CHALKboard
Antonio Rieser (03/29/23) Algebraic Topology for Graphs & Mesoscopic Spaces: Homotopy & Sheaf Theory
Title: Algebraic Topology for Graphs and Mesoscopic Spaces: Homotopy and Sheaf Theory Abstract: In this talk, we introduce the notion of a mesoscopic space: a metric space decorated with a privileged scale, and we survey recent developments in the algebraic topology of such spaces. Our ap
From playlist AATRN 2023
What is a Vector Space? (Abstract Algebra)
Vector spaces are one of the fundamental objects you study in abstract algebra. They are a significant generalization of the 2- and 3-dimensional vectors you study in science. In this lesson we talk about the definition of a vector space and give a few surprising examples. Be sure to su
From playlist Abstract Algebra
Patrizio Frosini (8/30/21): On the role of group equivariant non-expansive operators in TDA
Group equivariant non-expansive operators (GENEOs) have been recently introduced as mathematical tools for approximating data observers, when data are represented by real-valued or vector-valued functions. The use of these operators is based on the assumption that the interpretation of dat
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Convergence and Riemannian bounds on Lagrangian submanifolds - Jean-Philippe Chassé
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Title: Convergence and Riemannian bounds on Lagrangian submanifolds Speaker: Jean-Philippe Chassé Affiliation: UdeM Date: October 8, 2021 Abstract: Recent years have seen the appearance of a plethora of possible metrics on
From playlist PU/IAS Symplectic Geometry Seminar
Nicola Quercioli (1/13/21): Group equivariant non-expansive operators and their use in Deep Learning
Full Title: On the topological and geometrical properties of group equivariant non-expansive operators and their use in Deep Learning
From playlist ATMCS/AATRN 2020
Seminar In the Analysis and Methods of PDE (SIAM PDE): François Golse
Title: Quantum Dynamics and Optimal Transport Date: Thursday, February 3, 2022, 11:30 am ET Speaker: François Golse, École polytechnique, France Abstract: In 1979, Dobrushin explained how Monge’s theory of optimal transport (1781) can be used to prove the mean-field limit for the classica
From playlist Seminar In the Analysis and Methods of PDE (SIAM PDE)
Francesca Tombari (8/27/21): Decomposing simplicial complexes (without losing pieces)
When we decompose a simplicial complex and reassemble it, it might happen that the resulting complex has a different homotopy type from the initial one. However, it is sometimes possible to understand this change by looking at subcomplexes living in the intersection of the two decomposing
From playlist Vietoris-Rips Seminar
Measure Growth in Compact Simple Lie Groups - Yifan Jing
Special Year Research Seminar Topic: Measure Growth in Compact Simple Lie Groups Speaker: Yifan Jing Affiliation: University of Oxford Date: November 08, 2022 The celebrated product theorem says if A is a generating subset of a finite simple group of Lie type G, then |AAA| \gg \min \{ |A
From playlist Mathematics
Iosif Petrakis: Bishop spaces and the problem of constructivizing general topology
The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: According to Bishop (see [1], p.28), the constructivization of general topology is impeded by two obstacles. First, the classical notion of a topological space is not constru
From playlist Workshop: "Constructive Mathematics"
What is (a) Space? From Zero to Geo 1.5
What is space? In this video, we learn about the many different things that we might call "space". We come up with both a geometric and an algebraic definition, and the discussion also leads us to the important concept of subspaces. Sorry for how long this video took to make! I mention
From playlist From Zero to Geo
Introduction to Cylindrical Coordinates
This video introduces cylindrical coordinates and shows how to convert between cylindrical coordinates and rectangular coordinates. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
Worldwide Calculus: Euclidean Space
Lecture on 'Euclidean Space' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Spaces and Functions
Triangulated persistence categories - Jun Zhang
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Triangulated persistence categories Speaker: Jun Zhang Affiliation: Université de Montréal Date: September 25, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics