Topology (What is a Topology?)
What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b
From playlist Topology
In this video, I cover the notion of continuity, as used in topology. The beautiful thing is that this doesn't use epsilon-delta at all, and instead just something purely geometric. Enjoy this topology-adventure! Topology Playlist: https://youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGG
From playlist Topology
Symplectic topology and the loop space - Jingyu Zhao
Topic: Symplectic topology and the loop space Speaker: Jingyu Zhao, Member, School of Mathematics Time/Room: 4:45pm - 5:00pm/S-101 More videos on http://video.ias.edu
From playlist Mathematics
Algebraic topology: Introduction
This lecture is part of an online course on algebraic topology. This is an introductory lecture, where we give a quick overview of some of the invariants of algebraic topology (homotopy groups, homology groups, K theory, and cobordism). The book "algebraic topology" by Allen Hatcher men
From playlist Algebraic topology
François Petit (6/22/20): Ephemeral persistence modules and distance comparison
Title: Ephemeral persistence modules and distance comparison Abstract: Sheaf theoretic methods have been recently introduced to study persistent modules. Persistence homology studies filtered or multi-filtered topological spaces. The filtrations are indexed by the elements of an ordered
From playlist ATMCS/AATRN 2020
I define closed sets, an important notion in topology and analysis. It is defined in terms of limit points, and has a priori nothing to do with open sets. Yet I show the important result that a set is closed if and only if its complement is open. More topology videos can be found on my pla
From playlist Topology
Fernando Galaz Garcia: Three dimensional Alexandrov spaces with positive and non negative curvature
I will discuss the topological classification of closed three-dimensional Alexandrov spaces with positive or non-negative curvature, both in the Alexandrov and CD(K,N) sense. This is joint work with Luis Guijarro, Michael Munn and Qintao Deng. The lecture was held within the framework of
From playlist HIM Lectures: Follow-up Workshop to JTP "Optimal Transportation"
Lecture 17: Alexandrov's Theorem
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This lecture addresses the mathematical approaches for solving the decision problem for folding polyhedra. A proof of Alexandrov's
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
In this video, I introduce the order topology and prove that it is Hausdorff. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Analytic Geometry Over F_1 - Vladimir Berkovich
Vladimir Berkovich Weizmann Institute of Science March 10, 2011 I'll talk on work in progress on algebraic and analytic geometry over the field of one element F_1. This work originates in non-Archimedean analytic geometry as a result of a search for appropriate framework for so called skel
From playlist Mathematics
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This class introduces the pita form and Alexandrov-Pogorelov Theorem. D-forms are discussed with a construction exercise, followed
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Homotopy elements in the homotopy group π₂(S²) ≅ ℤ. Roman Gassmann and Tabea Méndez suggested some improvements to my original ideas.
From playlist Algebraic Topology
A topological view on the Monge-Ampere equation without convexity assumptions - Jonas Hirsch
Workshop on the h-principle and beyond Topic: A topological view on the Monge-Ampere equation without convexity assumptions Speaker: Jonas Hirsch Affiliation: University of Leipzig Date: November 4, 2021
From playlist Mathematics
Jürgen Jost (5/13/22): Geometry and Topology of Data
We link the basic concept of topological data analysis, intersection patterns of distance balls, with geometric concepts. The key notion is hyperconvexity, and we also explore some variants. Hyperconvexity in turn leads us to a new concept of generalized curvature for metric spaces. Curvat
From playlist Bridging Applied and Quantitative Topology 2022
Jürgen Jost (8/29/21): Geometry and Topology of Data
Data sets are often equipped with distances between data points, and thereby constitute a discrete metric space. We develop general notions of curvature that capture local and global properties of such spaces and relate them to topological concepts such as hyperconvexity. This also leads t
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Isoperimetry and boundaries with almost constant mean curvature - Francesco Maggi
Variational Methods in Geometry Seminar Topic: Isoperimetry and boundaries with almost constant mean curvature Speaker: Francesco Maggi Affiliation: The University of Texas at Austin; Member, School of Mathematics Date: February 12, 2019 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Clark Barwick - 2/3 Exodromy for ℓ-adic Sheaves
In joint work with Saul Glasman and Peter Haine, we proved that the derived ∞-category of constructible ℓ-adic sheaves ’is’ the ∞-category of continuous functors from an explicitly defined 1-category to the ∞-category of perfect complexes over ℚℓ. In this series of talks, I want to offer s
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Andreï Kolmogorov: un grand mathématicien au coeur d'un siècle tourmenté
Conférence grand public au CIRM Luminy Andreï Kolmogorov est un mathématicien russe (1903-1987) qui a apporté des contributions frappantes en théorie des probabilités, théorie ergodique, turbulence, mécanique classique, logique mathématique, topologie, théorie algorithmique de l'informati
From playlist OUTREACH - GRAND PUBLIC
Nekrashevych: Constructing simple groups using dynamical systems
We will show how minimal dynamical systems and etale groupoids can be used to construct finitely generated simple groups with prescribed properties. For example, one can show that there are uncountably many different growth types (in particular quasi-isometry classes) among finitely genera
From playlist Topology