This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
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
Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener
From playlist Topology
This video is about metric spaces and some of their basic properties.
From playlist Basics: Topology
What is a metric space? An example
This is a basic introduction to the idea of a metric space. I introduce the idea of a metric and a metric space framed within the context of R^n. I show that a particular distance function satisfies the conditions of being a metric.
From playlist Mathematical analysis and applications
Weird notions of "distance" || Intro to Metric Spaces
Visit https://brilliant.org/TreforBazett/ to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor Weird, fun
From playlist Cool Math Series
MAST30026 Lecture 2: Examples of spaces (Part 1)
I started with the definition of a metric space, we briefly discussed the example of Euclidean space (proofs next time) and then I started to explain a few natural metrics on the circle. Lecture notes: http://therisingsea.org/notes/mast30026/lecture2.pdf The class webpage: http://therisin
From playlist MAST30026 Metric and Hilbert spaces
Complete metric space: example & proof
This video discusses an example of particular metric space that is complete. The completeness is proved with details provided. Such ideas are seen in branches of analysis.
From playlist Mathematical analysis and applications
This video is about topological spaces and some of their basic properties.
From playlist Basics: Topology
Maxim Kontsevich - 4/4 Bridgeland Stability over Non-Archimedean Fields
Bridgeland stability structure/condition on a triangulated category is a vast generalization of the notion of an ample line bunlde (or polarization) in algebraic geometry. The origin of the notion lies in string theory, and is applicable to derived categories of coherent sheaves, quiver re
From playlist Maxim Kontsevitch - Bridgeland Stability over Non-Archimedean Fields
Nina Otter (4/23/19): The magnitude of a metric space
Title: The magnitude of a metric space Abstract: The magnitude is an isometric invariant of metric spaces that was introduced by Tom Leinster in 2010, and is currently the object of intense research. Magnitude encodes many invariants of a metric space such as volume, dimension, capacity,
From playlist AATRN 2019
David Meyer (1/30/18): Some algebraic stability theorems for generalized persistence modules
From an algebraic point of view, generalized persistence modules can be interpreted as finitely-generated modules for a poset algebra. We prove an algebraic analogue of the isometry theorem of Bauer and Lesnick for a large class of posets. This theorem shows that for such posets, the int
From playlist AATRN 2018
Maxim Kontsevich - 3/4 Bridgeland Stability over Non-Archimedean Fields
Bridgeland stability structure/condition on a triangulated category is a vast generalization of the notion of an ample line bunlde (or polarization) in algebraic geometry. The origin of the notion lies in string theory, and is applicable to derived categories of coherent sheaves, quiver re
From playlist Maxim Kontsevitch - Bridgeland Stability over Non-Archimedean Fields
Flow on quiver representations, nested logarithms, and weight filtrations... - Fabian Haiden
Speaker:Fabian Haiden Topic: Flow on quiver representations, nested logarithms, and weight filtrations in artinian categories Affiliation: Harvard Date: November 11, 2016
From playlist Mathematics
Graeme Segal: Wick rotation and the positivity of energy in quantum field theory
Talk by Graeme Segal in Global Noncommutative Geometry Seminar (Americas) on December 17, 2021. https://globalncgseminar.org/talks/tba-19/
From playlist Global Noncommutative Geometry Seminar (Americas)
Stephan Mescher (3/10/22): Geodesic complexity of Riemannian manifolds
Geodesic complexity is motivated by Farber’s notion of topological complexity of a space, which gives a topological description of the motion planning problem in robotics. Motivated by this, D. Recio-Mitter recently introduced geodesic complexity as an isometry invariant of geodesic spaces
From playlist Topological Complexity Seminar
Ulrich Bunke: Coarse homotopy theory and K-theory
Talke by Ulrich Bundle in Global Noncommutative Geometry Seminar (Americas) on September 30, 2022. https://globalncgseminar.org/talks/tba-36/
From playlist Global Noncommutative Geometry Seminar (Americas)
MAST30026 Lecture 1: What is space? (Part 1)
I started with three dictionary definitions of "space" and briefly discussed them, before moving on to a survey of the standard abstract notions of space used in mathematics, including metric, topological and Hilbert spaces. In the remainder of the lecture I discussed the connection betwee
From playlist MAST30026 Metric and Hilbert spaces
Parameters in indexed homology - Simon Cho
Workshop on Topology: Identifying Order in Complex Systems Topic: Parameters in indexed homology Speaker: Simon Cho Affiliation: University of Michigan Date: October 9, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics