This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
Introduction to Metric Spaces - Definition of a Metric. - The metric on R - The Euclidean Metric on R^n - A metric on the set of all bounded functions - The discrete metric
From playlist Topology
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
Algebraic Topology - 2 - Balls
Here we show that convex sets in RR^n which are compact with nonempty interior are homeomorphic to the n-ball --- the boundaries are (n-1)-spheres. Errata: In the one point compactification we need open neighborhoods of infinity to have compact complement. So a neighborhood at infinity is
From playlist Algebraic Topology
This video is about topological spaces and some of their basic properties.
From playlist Basics: Topology
A short video on terms such as Vector Space, SubSpace, Span, Basis, Dimension, Rank, NullSpace, Col space, Row Space, Range, Kernel,..
From playlist Tutorial 4
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
This video is about metric spaces and some of their basic properties.
From playlist Basics: Topology
Peter Scholze - Liquid vector spaces
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ (joint with Dustin Clausen) Based on the condensed formalism, we propose new foundations for real functional analysis, replacing complete locally convex vector spaces with a vari
From playlist Toposes online
Dustin Clausen: New foundations for functional analysis
Talk by Dustin Clausen in Global Noncommutative Geometry Seminar (Americas) on November 12, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Johnathan Bush (11/5/21): Maps of Čech and Vietoris–Rips complexes into euclidean spaces
We say a continuous injective map from a topological space to k-dimensional euclidean space is simplex-preserving if the image of each set of at most k+1 distinct points is affinely independent. We will describe how simplex-preserving maps can be useful in the study of Čech and Vietoris–Ri
From playlist Vietoris-Rips Seminar
Complex geometry of Teichmuller domains (Lecture 1) by Harish Seshadri
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
GPDE Workshop - Synthetic formulations - Cedric Villani
Cedric Villani IAS/ENS-France February 23, 2009 For more videos, visit http://video.ias.edu
From playlist Mathematics
A WEIRD VECTOR SPACE: Building a Vector Space with Symmetry | Nathan Dalaklis
We'll spend time in this video on a weird vector space that can be built by developing the ideas around symmetry. In the process of building a vector space with symmetry at its core, we'll go through a ton of different ideas across a handful of mathematical fields. Naturally, we will start
From playlist The New CHALKboard
Act globally, compute...points and localization - Tara Holm
Tara Holm Cornell University; von Neumann Fellow, School of Mathematics October 20, 2014 Localization is a topological technique that allows us to make global equivariant computations in terms of local data at the fixed points. For example, we may compute a global integral by summing inte
From playlist Mathematics
Kähler–Einstein metrics on Fano manifolds: variational and algebro-geometric – S. Boucksom – ICM2018
Algebraic and Complex Geometry | Analysis and Operator Algebras Invited Lecture 4.1 | 8.1 Kähler–Einstein metrics on Fano manifolds: variational and algebro-geometric aspects Sébastien Boucksom Abstract: I will describe a variational approach to the existence of Kähler–Einstein metrics o
From playlist Algebraic & Complex Geometry
Kai Cieliebak - Stein and Weinstein manifolds
Stein manifolds arise naturally in the theory of several complex variables. This talk will give an informal introduction to some of their topological and symplectic aspects such as: handlebody construction of Stein manifolds; their symplectic counterparts; Weinstein manifolds; flexibility
From playlist Not Only Scalar Curvature Seminar
Robert Ghrist, Lecture 3: Topology Applied III
27th Workshop in Geometric Topology, Colorado College, June 12, 2010
From playlist Robert Ghrist: 27th Workshop in Geometric Topology
Emanuel Milman: Functional Inequalities on sub-Riemannian manifolds via QCD
We are interested in obtaining Poincar ́e and log-Sobolev inequalities on domains in sub-Riemannian manifolds (equipped with their natural sub-Riemannian metric and volume measure). It is well-known that strictly sub-Riemannian manifolds do not satisfy any type of Curvature-Dimension condi
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
Calculus 3: Vector Calculus in 2D (17 of 39) What is the Position Vector?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the position vector. The position vector indicates the position of a particle relative to the origin. The position usually depends on, or is a function of, a parametric variable (ex. t
From playlist CALCULUS 3 CH 3 VECTOR CALCULUS