Bekenstein bound

Measure Theory 2.1 : Lebesgue Outer Measure

In this video, I introduce the Lebesgue outer measure, and prove that it is, in fact, an outer measure. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Measure Theory

Upper Bound

Upper and Lower Bound In this video, I define what it means for a set to be bounded above and bounded below. This will be useful in our definition of inf and sup. Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCZggpJZvUXnUzaw7fHCtoh

From playlist Real Numbers

Math 101 091517 Introduction to Analysis 07 Consequences of Completeness

Least upper bound axiom implies a "greatest lower bound 'axiom'": that any set bounded below has a greatest lower bound. Archimedean Property of R.

From playlist Course 6: Introduction to Analysis (Fall 2017)

Sum of limits

Sum of limits In this video, I give a very classical proof that the limit of the sum of two convergent sequences is the sum of the limit of each sequence. It's mathematical analysis at its finest, enjoy the show! Other examples of limits can be seen in the playlist below. Definition of

From playlist Sequences

How Much Information is in the Universe?

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/DonateSPACE There’s quite a bit of stuff in the universe, to put it mildly. You can further support us on Patreon at https://www.patreon.com/pbsspacetime Get your own Space Time

From playlist Understanding the Holographic Universe

Computing a Universe Simulation

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/DonateSPACE Physics seems to be telling us that it’s possible to simulate the entire universe on a computer smaller than the universe. You can further support us on Patreon at h

From playlist Space Time!

Lorenzo Zambotti: Bessel-like SPDEs

Abstract: I will discuss integration by parts formulae on the law of the Bessel bridge of dimension less than 3 and show how this allows to conjecture the form of an associated SPDE. The most relevant case is the dimension equal to 1, which is expected to be the scaling limit of critical w

From playlist Probability and Statistics

The Black Hole Entropy Enigma

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/DonateSPACE Thanks to CuriosityStream for supporting PBS Digital Studios. You can learn more at https://www.curiositystream.com/spacetime and use the code "spacetime" during the s

From playlist Understanding the Holographic Universe

Introduction to the Wasserstein distance

Title: Introduction to the Wasserstein distance Abstract: I give an introduction to the Wasserstein distance, which is also called the Kantorovich-Rubinstein, optimal transport, or earth mover's distance. In particular, I describe how the 1-Wasserstein distance is defined between probabil

From playlist Tutorials

Math 131 Fall 2018 092818 Closure, Relative Openness, Intro to Compact Sets1

From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)

What If Our Understanding of Gravity Is Wrong?

Thank you to CuriosityStream for supporting PBS. For more information go to https://curiositystream.thld.co/PBSSPACETIME Check Out @PBSVitals here: https://youtu.be/FOL0Hs8UcNs What if there is no such thing as dark matter? What if our understanding of gravity is just wrong? New work is

From playlist Dark Matter Explained!

Gilles Dowek : Informatique et physique : quelques interactions

Recording during the thematic meeting : "Algorithm and Programming" the May 2, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathemat

From playlist Mathematical Physics

Are there Infinite Versions of You?

PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateSPACE ↓ More info below ↓ Sign Up on Patreon to get access to the Space Time Discord! https://www.patreon.com/pbsspacetime Sign up for the mailing list to get episode notification

From playlist Many Worlds and the Multiverse Explained!

A New Perspective on Holographic Entanglement by Matthew Headrick

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

The limit is the limit is the limit is the limit

Here I evaluate a neat infinite limit with l'Hopital's rule... does it work though? Subscribe to my channel: https://youtube.com/drpeyam Check out my TikTok channel: https://www.tiktok.com/@drpeyam Follow me on Instagram: https://www.instagram.com/peyamstagram/ Follow me on Twitter: https

From playlist Calculus

Entropy Bounds, Light-sheets, and the Holographic Principle in Cosmology, part 1 - Raphael Bousso

Entropy Bounds, Light-sheets, and the Holographic Principle in Cosmology, part 1 Raphael Bousso University of California, Berkeley July 28, 2011

From playlist PiTP 2011

Entropy Bounds, Light-sheets, and the Holographic Principle... part 1 continued - Raphael Bousso

Entropy Bounds, Light-sheets, and the Holographic Principle in Cosmology, part 1 continued Raphael Bousso University of California, Berkeley July 28, 2011

From playlist PiTP 2011

A neat diagonal argument

Limit points are closed In this video, I present a very nice and surprising result about sequences, namely that the set of limit points of a sequence is a closed set. The beauty of this lies not in the fact, but in the proof, which uses an elegant diagonal argument. Enjoy! What is a limi

From playlist Sequences

Dispersive Estimates for Schroedinger's Equation with a Time-Dependent Potential - Marius Beceanu

Marius Beceanu Rutgers, The State University of New Jersey; Member, School of Mathematics January 15, 2013 I present some new dispersive estimates for Schroedinger's equation with a time-dependent potential, together with applications. For more videos, visit http://video.ias.edu

From playlist Mathematics

A modern take on the information paradox.... (Lecture - 03) by Ahmed Almheiri

INFOSYS-ICTS STRING THEORY LECTURES A MODERN TAKE ON THE INFORMATION PARADOX AND PROGRESS TOWARDS ITS RESOLUTION SPEAKER: Ahmed Almheiri (Institute for Advanced Study, Princeton) DATE: 30 September 2019 to 03 October 2019 VENUE: Emmy Noether Seminar Room, ICTS Bangalore Lecture 1: Mond

From playlist Infosys-ICTS String Theory Lectures