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
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
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
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?
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 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
The structure of noncollapsed Gromov-Hausdorff limit spaces - Jeff Cheeger [2017]
slides for this talk: https://drive.google.com/file/d/1pvkn4Qew5ZHrDpvs9txzFOsFFDqYfA3E/view?usp=sharing Name: Jeff Cheeger Event: Workshop: Geometry of Manifolds Event URL: view webpage Title: The structure of noncollapsed Gromov-Hausdorff limit spaces with Ricci Curvature bounded below
From playlist Mathematics
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
R. Ghezzi - Volume measures in non equiregular sub-Riemannian manifolds
In this talk we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it to a smooth volume. First we give the Lebesgue decomposition of the Hausdorff volume. Then we focus on the regular part, show that it is not commensurable with a smooth volume and give
From playlist Journées Sous-Riemanniennes 2017
Quantitative propagation for solutions of elliptic equations – A. Logunov & E. Malinnikova – ICM2018
Partial Differential Equations | Geometry Invited Lecture 10.11 | 5.12 Quantitative propagation of smallness for solutions of elliptic equations Alexander Logunov & Eugenia Malinnikova Abstract: Let u be a solution to an elliptic equation div(A∇u)=0 with Lipschitz coefficients in ℝⁿ. Ass
From playlist Geometry
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
Yevgeny Liokumovich (9/10/21): Urysohn width, isoperimetric inequalities and scalar curvature
There exists a positive constant c(n) with the following property. If M is a metric space, such that every ball B of radius 1 in M has Hausdorff n-dimensional measure less than c(n), then there exists a continuous map f from M to (n-1)-dimensional simplicial complex, such that every pre-im
From playlist Vietoris-Rips Seminar
Christina Sormani: A Course on Intrinsic Flat Convergence part 1
Intrinsic Flat Convergence was first introduced in joint work with Stefan Wenger building upon work of Ambrosio-Kirchheim to address a question proposed by Tom Ilmanen. In this talk, I will present an overview of the initial paper on the topic [JDG 2011]. I will briefly describe key examp
From playlist HIM Lectures 2015
Manifolds 1.1 : Basic Definitions
In this video, I give the basic intuition and definitions of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Manifolds
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
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
Hierarchies of contact manifolds - Zhengyi Zhou
Short Talks by Postdoctoral Members Topic: Hierarchies of contact manifolds Speaker: Zhengyi Zhou Affiliation: Member, School of Mathematics Date: October 1, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics