In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself in an approximate "X" shape. The points on the floor where it does this are one kind of singularity, the double point: one bit of the floor corresponds to more than one bit of string. Perhaps the string will also touch itself without crossing, like an underlined "U". This is another kind of singularity. Unlike the double point, it is not stable, in the sense that a small push will lift the bottom of the "U" away from the "underline". Vladimir Arnold defines the main goal of singularity theory as describing how objects depend on parameters, particularly in cases where the properties undergo sudden change under a small variation of the parameters. These situations are called perestroika (Russian: перестройка), bifurcations or catastrophes. Classifying the types of changes and characterizing sets of parameters which give rise to these changes are some of the main mathematical goals. Singularities can occur in a wide range of mathematical objects, from matrices depending on parameters to wavefronts. (Wikipedia).
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From playlist Science Unplugged: Black Holes
Are there physicists trying to understand singularities?
Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu
From playlist Science Unplugged: Black Holes
Stuff From The Future - What is the Singularity?
Will computers of the future have the ability to design themselves? Is it possible that human beings may be able to download their consciousness onto machines? Join TechStuff's Jonathan Strickland as he takes a closer look at the singularity http://howstuffworks.com http://itunes.apple
From playlist Stuff From the Future
Complex analysis: Singularities
This lecture is part of an online undergraduate course on complex analysis. We discuss the different sorts of singularities of a holomorphic function (removable singularities, poles, essential singularities, branch-points, limits of singularities, natural boundaries) and give examples of
From playlist Complex analysis
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
The Place Where TIME Stands Still...
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From playlist Waves And Theories
Noam Chomsky on AI: The Singularity is Science Fiction!
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The Technological Singularity Explained Try Dashlane on your first device for FREE: http://dashlane.com/aperture pls get me to 10k on instagram!: https://www.instagram.com/mcewen/ The technological singularity is one of the most popular topics in computer science today. The implications
From playlist Science & Technology 🚀
What is a Singularity, Exactly?
The singularity. Both the black hole singularity and the AI singularity. Predictions by Ray Kurzweil. Hi! I'm Jade. Subscribe to Up and Atom for new physics, math and computer science videos every week! *SUBSCRIBE TO UP AND ATOM* https://www.youtube.com/c/upandatom Visit the Up and Ato
From playlist AI
Statistical mechanics of deep learning - Surya Ganguli
Workshop on Theory of Deep Learning: Where next? Topic: Statistical mechanics of deep learning Speaker: Surya Ganguli Affiliation: Stanford University Date: October 18, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Emergence of singularities from decoherence in a Josephson junction by Duncan H J O'Dell
Open Quantum Systems DATE: 17 July 2017 to 04 August 2017 VENUE: Ramanujan Lecture Hall, ICTS Bangalore There have been major recent breakthroughs, both experimental and theoretical, in the field of Open Quantum Systems. The aim of this program is to bring together leaders in the Open Q
From playlist Open Quantum Systems
Must space-time be singular? by Ward Struyve
21 November 2016 to 10 December 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Quantum Theory has passed all experimental tests, with impressive accuracy. It applies to light and matter from the smallest scales so far explored, up to the mesoscopic scale. It is also a necessary ingredie
From playlist Fundamental Problems of Quantum Physics
R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions (vt)
We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow. Under a natural non-collapsing condition, this limiting flow is smooth on the complement of a sing
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions
We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow. Under a natural non-collapsing condition, this limiting flow is smooth on the complement of a sing
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Sandipan Kundu - 1/2 Causality in Conformal Field Theory
https://indico.math.cnrs.fr/event/3308/ Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In these pedagogical lectures, I will explore causality constraints on conformal field theory. First,
From playlist Sandipan Kundu - Three Lectures on Causality in Conformal Field Theory
Knot Categorification From Mirror Symmetry (Lecture- 1) by Mina Aganagic
PROGRAM QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
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The Weak Cosmic Censorship Conjecture: Status Report by Pau Figueras
PROGRAM Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (ONLINE) ORGANIZERS: David Berenstein (UCSB), Simon Catterall (Syracuse University), Masanori Hanada (University of Surrey), Anosh Joseph (IISER, Mohali), Jun Nishimura (KEK Japan), David Sc
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (Online)
A Holographic View of Singularities by Eliezer Rabinovici
11 January 2017 to 13 January 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru String theory has come a long way, from its origin in 1970's as a possible model of strong interactions, to the present day where it sheds light not only on the original problem of strong interactions, but
From playlist String Theory: Past and Present
Duality in Higher Categories-I by Pranav Pandit
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)