Low-dimensional topology

What is a closed set ?

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

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

Topology 1.1 : Open Sets of Reals

In this video, I give a definition of the open sets on the real numbers. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Topology

Topology 1.7 : More Examples of Topologies

In this video, I introduce important examples of topologies I didn't get the chance to get to. This includes The discrete and trivial topologies, subspace topology, the lower-bound and K topologies on the reals, the dictionary order, and the line with two origins. I also introduce (again)

From playlist Topology

Definition of a Topological Space

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space

From playlist Topology

Problem 1-general topology

From playlist MATH3701 - Higher Topology and Differential Geometry

Algebraic Topology - 5.1 - Mappings Spaces and the Compact Open Topology

We define the compact open topology on mapping spaces.

From playlist Algebraic Topology

Topology: Metric Spaces

This video is about metric spaces and some of their basic properties.

From playlist Basics: Topology

Topology: Topological Spaces

This video is about topological spaces and some of their basic properties.

From playlist Basics: Topology

An introduction to persistent homology

Title: An introduction to persistent homology Venue: Webinar for DELTA (Descriptors of Energy Landscape by Topological Analysis Abstract: This talk is an introduction to applied and computational topology, in particular as related to the study of energy landscapes arising in chemistry. W

From playlist Tutorials

Dominic Else - Emergent Symmetries and Anomalies in Metals: Luttinger's Theorem and Beyond

Séminaire organisé le 23 novembre 2021 Metals are an interesting class of gapless quantum many-body systems. Many metals are described by the famous "Fermi liquid theory" at low temperatures, but there are also many metallic materials for which Fermi liquid theory is an inadequate descrip

From playlist Quantum Encounters Seminar - Quantum Information, Condensed Matter, Quantum Field Theory

Henry Adams (5/3/22): Topology in Machine Learning

Abstract: How do you "vectorize" geometry, i.e., extract it as a feature for use in machine learning? One way is persistent homology, a popular technique for incorporating geometry and topology in data analysis tasks. I will survey applications arising from materials science, computer visi

From playlist Tutorials

Electrical properties of quantum states at the boundary of graphene by Arindam Ghosh

DISCUSSION MEETING : EDGE DYNAMICS IN TOPOLOGICAL PHASES ORGANIZERS : Subhro Bhattacharjee, Yuval Gefen, Ganpathy Murthy and Sumathi Rao DATE & TIME : 10 June 2019 to 14 June 2019 VENUE : Madhava Lecture Hall, ICTS Bangalore Topological phases of matter have been at the forefront of r

From playlist Edge dynamics in topological phases 2019

Large-Spin Magnetic Impurity near a 2D Topological Edge by Moshe Goldstein

DISCUSSION MEETING : EDGE DYNAMICS IN TOPOLOGICAL PHASES ORGANIZERS : Subhro Bhattacharjee, Yuval Gefen, Ganpathy Murthy and Sumathi Rao DATE & TIME : 10 June 2019 to 14 June 2019 VENUE : Madhava Lecture Hall, ICTS Bangalore Topological phases of matter have been at the forefront of r

From playlist Edge dynamics in topological phases 2019

John Milnor: Spheres

This lecture was held by Abel Laureate John Milnor at The University of Oslo, May 25, 2011 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2011 1. "Spheres" by Abel Laureate John Milnor, Institute for Mathematical

From playlist Abel Lectures

Topological effects in metals - Moore

Joel Moore November 7, 2015 The recent advances in our understanding of topological states of free-fermion insulators give some valuable concepts and tools for the analysis of metals. The first part of this talk focuses on low-energy electrodynamic responses of simple metals, including th

From playlist Mathematics

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

Emergent Symmetries, Luttinger's Theorem and 't Hooft Anomalies in Metals by Senthil Todadri

DISCUSSION MEETING TOPOLOGICAL ASPECTS OF STRONG CORRELATIONS AND GAUGE THEORIES (ONLINE) ORGANIZERS: Rob Pisarski (Brookhaven National Laboratory, USA), Sumathi Rao (HRI, India), Soeren Schlichting (Bielefeld University, Germany) and Sayantan Sharma (IMSc, India) DATE: 06 September 202

From playlist Topological aspects of strong correlations and gauge theories (ONLINE)

Algebraic Topology - 5.2 - Mapping Spaces and the Compact Open Topology

We give an example of how the metric topology agrees with the compact open topology on Top(X,Y) when X is compact and Y is metric.

From playlist Algebraic Topology

Pierrick Bousseau - The Skein Algebra of the 4-punctured Sphere from Curve Counting

The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on the SL_2 character of a topological surface. I will explain how to realize the skein algebra of the 4-punctured sphere as the output of a mirror symmetry construction based on higher genus Gromov-Wi

From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory