Hausdorff distance

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

What is the distance between two sets of points? | Hausdorff Distance

What is the distance between two sets of points is a non-trivial question that has applications all over the place, from bioinformatics and computer science to fractal geometry. In this video, I'll give a bit of motivation, introduce the delta expansion of a set and then give the distance

From playlist The New CHALKboard

Impressionen Bonner Mathematikturnier 2021

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

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

Sunhyuk Lim (9/24/21): The Gromov-Hausdorff distance between spheres

We provide general upper and lower bounds for the Gromov-Hausdorff distance d_GH(S^m,S^n) between spheres S^m and S^n (endowed with the round metric) for m less than n, with both integers between 0 and infinity, inclusive. Some of these lower bounds are based on certain topological ideas r

From playlist Vietoris-Rips Seminar

Facundo Mémoli (5/2/21): The Gromov-Hausdorff distance between spheres

The Gromov-Hausdorff distance is a fundamental tool in Riemanian geometry, and also in applied geometry and topology. Whereas it is often easy to estimate the value of the distance between two given metric spaces, its precise value is rarely easy to determine. In this talk I will describe

From playlist TDA: Tutte Institute & Western University - 2021

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

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

Henry Adams (3/22/22): Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes

The Gromov-Hausdorff distance between two metric spaces is an important tool in geometry, but it is difficult to compute. For example, the Gromov-Hausdorff distance between unit spheres of different dimensions is unknown in nearly all cases. I will introduce recent work by Lim, Mémoli, and

From playlist Vietoris-Rips Seminar

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

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

C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1

We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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)

C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1 (version temporaire)

We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

Über das Leben Felix Hausdorffs

Leben und Werk von Felix Hausdorff stellten am Aktionstag Mathematik Dr. Michael Meier, ehem. Geschäftsführer des Hausdorff Centers, und Pascal Lamy, Absolvent der Mathematik und der Geschichtswissenschaft, im Herbst 2018 vor. Den Namen des Mathematikers, Literaten und Philosophen trägt he

From playlist Hausdorff Center goes public

Christina Sormani: A Course on Intrinsic Flat Convergence part 3

The lecture was held within the framework of the Hausdorff Trimester Program: Optimal Transportation and the Workshop: Winter School & Workshop: New developments in Optimal Transport, Geometry and Analysis

From playlist HIM Lectures 2015