An introduction to the Gromov-Hausdorff distance
Title: An introduction to the Gromov-Hausdorff distance Abstract: We give a brief introduction to the Hausdorff and Gromov-Hausdorff distances between metric spaces. The Hausdorff distance is defined on two subsets of a common metric space. The Gromov-Hausdorff distance is defined on any
From playlist Tutorials
Hausdorff Example 1: Cofinite Topology
Point Set Topology: We recall the notion of a Hausdorff space and consider the cofinite topology as a source of non-Hausdorff examples. We also note that this topology is always compact.
From playlist Point Set Topology
Hausdorff Example 3: Function Spaces
Point Set Topology: For a third example, we consider function spaces. We begin with the space of continuous functions on [0,1]. As a metric space, this example is Hausdorff, but not complete. We consider Cauchy sequences and a possible completion.
From playlist Point Set Topology
MAST30026 Lecture 11: Hausdorff spaces (Part 1)
I introduced the Hausdorff condition, proved some basic properties, discussed the "real line with a double point" as an example of a non-Hausdorff space, proved that a compact subspace of a Hausdorff space is closed, and that continuous bijections from compact to Hausdorff spaces are homeo
From playlist MAST30026 Metric and Hilbert spaces
Algebraic Topology - 1 - Compact Hausdorff Spaces (a Review of Point-Set Topology)
This is mostly a review point set topology. In general it is not true that a bijective continuous map is invertible (you need to worry about the inverse being continuous). In the case that your spaces are compact hausdorff this is true! We prove this in this video and review necessary fac
From playlist Algebraic Topology
Hausdorff School: Lecture by Jean-Pierre Bourguignon
Inauguration of the Hausdorff School The “Hausdorff School for Advanced Studies in Mathematics” is an innovative new program for postdocs by the Hausdorff Center. The official inauguration took place on October 20, 2015. Lecture by Jean-Pierre Bourguignon on "Sound, Shape, and Harmony –
From playlist Inauguration of Hausdorff School 2015
Hausdorff Center for Mathematics
The Hausdorff Center for Mathematics (HCM) capitalizes on a broad vision of mathematics, ranging from pure mathematics, to contributions to quantative modeling in economics and the natural sciences, to industrial applications. HCM strives to serve the international mathematical community a
From playlist Hausdorff Center goes public
Hausdorff School: Introduction by Karl-Theodor Sturm
Presentation of the Hausdorff School by Karl-Theodor Sturm, coordinator of the Hausdorff Center. The “Hausdorff School for Advanced Studies in Mathematics” is an innovative new program for postdocs by the Hausdorff Center. The official inauguration took place on October 20, 2015.
From playlist Inauguration of Hausdorff School 2015
MAST30026 Lecture 12: Function spaces (Part 3)
We continued the discussion of the compact-open topology on function spaces. Guided by Part 2 we defined this topology, and got about half way through the proof that the adjunction property (aka the exponential law) holds when function spaces are given this topology. Lecture notes: http:/
From playlist MAST30026 Metric and Hilbert spaces
MAST30026 Lecture 12: Function spaces (Part 4)
We completed the proof that the adjunction property holds for the space of continuous functions from a locally compact Hausdorff space, reminded ourselves of some of the immediate consequences of this theorem, and then began motivating the construction of a metric on function spaces. Lect
From playlist MAST30026 Metric and Hilbert spaces
Sergey Dorogovtsev - Complex network approach to evolving manifolds and simplicial complexes
https://indico.math.cnrs.fr/event/3475/attachments/2180/2574/Dorogovtsev_GomaxSlides.pdf
From playlist Google matrix: fundamentals, applications and beyond
Schemes 5: Definition of a scheme
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We give some historical background, then give the definition of a scheme and some simple examples, and finish by explaining the origin of the word "spectrum".
From playlist Algebraic geometry II: Schemes
MAST30026 Lecture 18: Banach spaces (Part 1)
There are many Lipschitz equivalent metrics on Euclidean space, apart from the sup-metric (which we have successfully generalised to function spaces) there are also metrics defined using sums. To generalise those, we need integrals, and the resulting theory leads to Banach spaces. In this
From playlist MAST30026 Metric and Hilbert spaces
Geometry of Surfaces - Topological Surfaces Lecture 1 : Oxford Mathematics 3rd Year Student Lecture
This is the first of four lectures from Dominic Joyce's 3rd Year Geometry of Surfaces course. The four lectures cover topological surfaces and conclude with a big result, namely the classification of surfaces. This lecture provides an introduction to the course and to topological surfaces.
From playlist Oxford Mathematics Student Lectures - Geometry of Surfaces
What is a Manifold? Lesson 6: Topological Manifolds
Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.
From playlist What is a Manifold?
Fitting a manifold to noisy data by Hariharan Narayanan
DISCUSSION MEETING THE THEORETICAL BASIS OF MACHINE LEARNING (ML) ORGANIZERS: Chiranjib Bhattacharya, Sunita Sarawagi, Ravi Sundaram and SVN Vishwanathan DATE : 27 December 2018 to 29 December 2018 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore ML (Machine Learning) has enjoyed tr
From playlist The Theoretical Basis of Machine Learning 2018 (ML)
Geometry of Surfaces - Topological Surfaces Lecture 2 : Oxford Mathematics 3rd Year Student Lecture
This is the second of four lectures from Dominic Joyce's 3rd Year Geometry of Surfaces course. The four lectures cover topological surfaces and conclude with a big result, namely the classification of surfaces. This lectures covers building topological surfaces by gluing sides of polygons.
From playlist Oxford Mathematics Student Lectures - Geometry of Surfaces
Hausdorff School für Mathematik-Nachwuchs eröffnet
Die Hausdorff School ist ein neuartiges, strukturiertes Ausbildungsprogramm für promovierte Nachwuchswissenschaftler, errichtet vom Hausdorff Center for Mathematics der Universität Bonn. Vor dem Festakt sprach uni-bonn.tv mit dem Rektor der Universität, Prof. Dr. Michael Hoch. Team: Marcu
From playlist Inauguration of Hausdorff School 2015
Introduction to Scalar Curvature and Convergence - Christina Sormani
Emerging Topics Working Group Topic: Introduction to Scalar Curvature and Convergence Speaker: Christina Sormani Affilaition: IAS Date: October 15, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics