What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Projection Theorem | Special Case of the Wigner–Eckart Theorem
The projection theorem is a special case of the Wigner–Eckart theorem, which generally involves spherical tensor operators. If we consider one example of a spherical tensor operator, a rank-1 spherical tensor, we can derive a powerful theorem, which states that expectation values of vector
From playlist Quantum Mechanics, Quantum Field Theory
Vortices on Non-compact Riemann Surfaces by Sushmita Venugopalan
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
Divergence Theorem. In this video, I give an example of the divergence theorem, also known as the Gauss-Green theorem, which helps us simplify surface integrals tremendously. It's, in my opinion, the most important theorem in multivariable calculus. It is also extremely useful in physics,
From playlist Vector Calculus
Should we get rid of standardized testing? - Arlo Kempf
Download a free audiobook and support TED-Ed's nonprofit mission: http://www.audible.com/teded Check out Todd Rose's "The End of Average: How We Succeed in a World That Values Sameness": https://shop.ed.ted.com/collections/ted-ed-book-recommendations/products/the-end-of-average View full
From playlist New TED-Ed Originals
Free ebook http://tinyurl.com/EngMath A short tutorial on how to apply Gauss' Divergence Theorem, which is one of the fundamental results of vector calculus. The theorem is stated and we apply it to a simple example.
From playlist Several Variable Calculus / Vector Calculus
Emily Cliff: Hilbert Schemes Lecture 6
SMRI Seminar Series: 'Hilbert Schemes' Lecture 6 GIT stability, quiver representations, & Hilbert schemes Emily Cliff (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to
From playlist SMRI Course: Hilbert Schemes
In this video, I present another example of Stokes theorem, this time using it to calculate the line integral of a vector field. It is a very useful theorem that arises a lot in physics, for example in Maxwell's equations. Other Stokes Example: https://youtu.be/-fYbBSiqvUw Yet another Sto
From playlist Vector Calculus
Conformal Blocks for Galois Covers of Algebraic Curves by Shrawan Kumar
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 Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Vector calculus review - divergence theorem
Lectures for Transport Phenomena course at Olin College. This lecture derives and explains the divergence theorem
From playlist Lectures for Transport Phenomena course
We present a proof of the Hopf-Rinow theorem. For more details see do Carmo's "Riemannian geometry" Chapter 7.
From playlist Differential geometry
The Bogomolov-Gieseker inequality and geography of moduli (Lecture 2) by Carlos Simpson
INFOSYS-ICTS RAMANUJAN LECTURES EXPLORING MODULI SPEAKER: Carlos Simpson (Université Nice-Sophia Antipolis, France) DATE: 10 February 2020 to 14 February 2020 VENUE: Madhava Lecture Hall, ICTS Campus Lecture 1: Exploring Moduli: basic constructions and examples 4 PM, 10 February 2020
From playlist Infosys-ICTS Ramanujan Lectures
Hajime Ishihara: The constructive Hahn Banach theorem, revisited
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: The Hahn-Banach theorem, named after the mathematicians Hans Hahn and Stefan Banach who proved it independently in the late 1920s, is a central tool in functional analys
From playlist Workshop: "Constructive Mathematics"
I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is
From playlist Series
The EM Drive: Fact or Fantasy?
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/DonateSPACE Because you demanded it … we break down the EM Drive! Support us on Patreon! https://www.patreon.com/pbsspacetime Get your own Space Time tshirt at http://bit.ly/1Ql
From playlist The Real Science of Warp Drives, Wormoholes and Faster Than Light (FTL) Travel
Algorithmic invariant theory - Visu Makam
Optimization, Complexity and Invariant Theory Topic: Algorithmic invariant theory Speaker: Visu Makam Affiliation: University of Michigan Date: June 6. 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
While there are so many reasons to remember Abraham Lincoln as the sixteenth president, he was more than a president, he was a singular personality, one of the most unique of the 45 men who have led the nation. Check out our new community for fans and supporters! https://thehistoryguygui
From playlist The Presidents
R. Lazarsfeld: The Equations Defining Projective Varieties. Part 2
The lecture was held within the framework of the Junior Hausdorff Trimester Program Algebraic Geometry. (9.1.2014)
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Dominated Convergence Theorem In this video, I present the single, most important fact from analysis that you need to know: The Dominated Convergence Theorem. It is a nice theorem that allows us to pass under the limit inside of an integral. The beauty of it is that its assumptions are ve
From playlist Real Analysis
Robert Lazarsfeld: Cayley-Bacharach theorems with excess vanishing
A classical result usually attributed to Cayley and Bacharach asserts that if two plane curves of degrees c and d meet in cd points, then any curve of degree (c + d - 3) passing through all but one of these points must also pass through the remaining one. In the late 1970s, Griffiths and H
From playlist Algebraic and Complex Geometry