Definition of a Topological Space
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From playlist Topology
Dan Guralnik (3/23/2023): Wanted: Topologists for Autonomous Robots Community
Topological Complexity (TC) addresses a foundational problem in Robotics from the 2nd half of the 20th century: Quantify the complexity of planning continuous paths through a topological space, regarded as the configuration/state space of a programmable synthetic system. Technological bre
From playlist Topological Complexity Seminar
This video is about topological spaces and some of their basic properties.
From playlist Basics: Topology
Topological Spaces: The Subspace Topology
Today, we discuss the subspace topology, which is a useful tool to construct new topologies.
From playlist Topology & Manifolds
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
Cyclic Quadrilateral: Proof Hint!
Link: https://www.geogebra.org/m/KYdypjws
From playlist Geometry: Dynamic Interactives!
Lecture 14: The Definition of TC
In this video, we finally give the definition of topological cyclic homology. In fact, we will give two definitions: the first is abstract in terms of a mapping spectrum spectrum in cyclotomic spectra and then we unfold this to a concrete definition on terms of negative topological cyclic
From playlist Topological Cyclic Homology
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
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
Commutative algebra 36 Artin Rees lemma
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we state and prove the Artin-Rees lemma, which states that the restriction of an stable I-adic filtration (of
From playlist Commutative algebra
Jens Hemelaer: Toposes in arithmetic noncommutative geometry
Talk by Jens Hemelaer in Global Noncommutative Geometry Seminar (Americas) on February 5, 2021
From playlist Global Noncommutative Geometry Seminar (Americas)
The Optimality of the Interleaving Distance on Multidimensional... Modules - Michael Lesnick
Michael Lesnick Stanford University; Member, School of Mathematics, IAS March 6, 2013 Persistent homology is a central object of study in applied topology. It offers a flexible framework for defining invariants, called barcodes, of point cloud data and of real valued functions. Many of the
From playlist Mathematics
Dustin Clausen: New foundations for functional analysis
Talk by Dustin Clausen in Global Noncommutative Geometry Seminar (Americas) on November 12, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Lecture 12: Classifying topoi (Part 1)
This is the first of several talks on the subject of classifying topoi. I began with a brief reminder of the overall picture from the first talk, i.e. what are classifying topoi and why do we care (from the point of view of organising mathematics). Then I spent some time talking about tens
From playlist Topos theory seminar
Ezra Miller (12/4/2018): Real multiparameter persistent homology
Persistent homology with multiple continuous parameters presents fundamental challenges different from those arising with one real or multiple discrete parameters. Existing algebraic theories apply either for discrete parameters or for one continuous parameter. In part, the difficulty ar
From playlist AATRN 2018
Interactive visualization of 2-D persistence modules - Lesnick
Michael Lesnick Columbia University November 7, 2015 In topological data analysis, we often study data by associating to the data a filtered topological space, whose structure we can then examine using persistent homology. However, in many settings, a single filtered space is not a rich en
From playlist Mathematics
Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry Part 2
At the start of the 20th century, David Hilbert asked which representations can arise by studying the monodromy of Fuchsian equations. This question was the starting point for a beautiful circle of ideas relating the topology of a complex algebraic variety X to the study of algebraic diffe
From playlist Felix Klein Lectures 2022
Peter Bubenik - Lecture 3 - TDA: Multiple Parameters
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Peter Bubenik, University of Florida Title: TDA - Multiple Parameters Abstract: The final talk will bring us to the multiparameter setting - a topic of great practical interest and a subject of current research. I will dis
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
Steven Kleiman - "Equisingularity of germs of isolated singularities"
Steven Kleiman delivers a research lecture at the Worldwide Center of Mathematics.
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Peter Bubenik (6/2/20): Topological data analysis for biological images
Title: Topological data analysis for biological images Abstract: I will introduce topological data analysis and show how it may be combined with machine learning to analyze certain biological images. Using a small collection of high-resolution images of a cell's actin cytoskeleton, we are
From playlist SIAM Topological Image Analysis 2020