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
David Morrison - WHAT IS … F-theory? [2014]
Dave Morrison Event: SCGP Weekly Talk Title: WHAT IS … F-theory? Date: 2014-09-09 @1:00 PM Location: 102 Abstract: In the spirit of the “WHAT IS …” series of articles in the Notices of the American Mathematical Society, I will give a description of F-theory from first priniciples. On the
From playlist Mathematics
Geometers Abandoned 2,000 Year-Old Math. This Million-Dollar Problem was Born - Hodge Conjecture
The Hodge Conjecture is one of the deepest problems in analytic geometry and one of the seven Millennium Prize Problems worth a million dollars, offered by the Clay Mathematical Institute in 2000. It consists of drawing shapes known topological cycles on special surfaces called projective
From playlist Math
Ptolemy's theorem and generalizations | Rational Geometry Math Foundations 131 | NJ Wildberger
The other famous classical theorem about cyclic quadrilaterals is due to the great Greek astronomer and mathematician, Claudius Ptolemy. Adopting a rational point of view, we need to rethink this theorem to state it in a purely algebraic way, without resort to `distances' and the correspon
From playlist Math Foundations
Weil conjectures 4 Fermat hypersurfaces
This talk is part of a series on the Weil conjectures. We give a summary of Weil's paper where he introduced the Weil conjectures by calculating the zeta function of a Fermat hypersurface. We give an overview of how Weil expressed the number of points of a variety in terms of Gauss sums. T
From playlist Algebraic geometry: extra topics
The Graph Removal Lemma - Jacob Fox
Jacob Fox Massachusetts Institute of Technology November 8, 2010 Let H be a fixed graph with h vertices. The graph removal lemma states that every graph on n vertices with o(nh) copies of H can be made H-free by removing o(n2) edges. We give a new proof which avoids Szemeredi's regularity
From playlist Mathematics
A Beautiful Proof of Ptolemy's Theorem.
Ptolemy's Theorem seems more esoteric than the Pythagorean Theorem, but it's just as cool. In fact, the Pythagorean Theorem follows directly from it. Ptolemy used this theorem in his astronomical work. Google for the historical details. Thanks to this video for the idea of this visual
From playlist Mathy Videos
1. A bridge between graph theory and additive combinatorics
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX In an unsuccessful attempt to prove Fermat's last theorem
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Weil conjectures 2: Functional equation
This is the second lecture about the Weil conjectures. We show that the Riemann-Roch theorem implies the rationality and functional equation of the zeta function of a curve over a finite field.
From playlist Algebraic geometry: extra topics
The ABC Conjecture, Brian Conrad (Stanford) [2013]
slides for this talk: https://drive.google.com/file/d/1J04zXCQYgn9MdgDUo63rH719cruiQJVo/view?usp=sharing The ABC Conjecture Brian Conrad [Stanford University] Stony Brook Mathematics Colloquium Video September 12, 2013 http://www.math.stonybrook.edu/Videos/Colloquium/video_slides.php?
From playlist Number Theory
“Gauss sums and the Weil Conjectures,” by Bin Zhao (Part 4 of 8)
“Gauss sums and the Weil Conjectures,” by Bin Zhao. The topics include will Gauss sums, Jacobi sums, and Weil’s original argument for diagonal hypersurfaces when he raised his conjectures. Further developments towards the Langlands program and the modularity theorem will be mentioned at th
From playlist CTNT 2016 - ``Gauss sums and the Weil Conjectures" by Bin Zhao
Rob Kusner: Willmore stability and conformal rigidity of minimal surfaces in S^n
A minimal surface M in the round sphere S^n is critical for area, as well as for the Willmore bending energy W=∫∫(1+H^2)da. Willmore stability of M is equivalent to a gap between −2 and 0 in its area-Jacobi operator spectrum. We show the W-stability of M persists in all higher dimensional
From playlist Geometry
Size Comparison of the Universe 2021
From the Planck scale to the cosmic scale, the size comparison of the universe will show you just how large our universe is! This is an update to my previous size comparison video published on the same date in 2019. Six songs, three AWESOME composers, check out their channels for their mu
From playlist Size Comparison of the Entire Universe
“Gauss sums and the Weil Conjectures,” by Bin Zhao (Part 7 of 8)
“Gauss sums and the Weil Conjectures,” by Bin Zhao. The topics include will Gauss sums, Jacobi sums, and Weil’s original argument for diagonal hypersurfaces when he raised his conjectures. Further developments towards the Langlands program and the modularity theorem will be mentioned at th
From playlist CTNT 2016 - ``Gauss sums and the Weil Conjectures" by Bin Zhao
Dmitryi Bilyk: Uniform distribution, lacunary Fourier series, and Riesz products
Uniform distribution theory, which originated from a famous paper of H. Weyl, from the very start has been closely connected to Fourier analysis. One of the most interesting examples of such relations is an intricate similarity between the behavior of discrepancy (a quantitative measure of
From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"
The Curse of Oak Island: MAP DISCOVERY REVEALS HIDDEN HATCH (Part 1) (Season 4) | History
Love The Curse Of Oak Island? Stay up to date on all of your favorite History Channel shows at https://history.com/schedule Rick, Marty, and the team examine a French map from 1347 that correlates perfectly with Oak Island, pointing to a secret hatch. Could this be a major step in finding
From playlist The Curse of Oak Island: Season 4 | History
Sasaki geometry and positive curvature - Song Sun [2012]
Abstract: We classify simply connected compact Sasaki manifolds with positive transverse bisectional curvature. In particular, the moduli space of all such manifolds can be contracted to a point—the standard round sphere. This provides an alternative proof of the Mori-Siu-Yau theorem on Fr
From playlist Mathematics
F. Schulze - Mean curvature flow with generic initial data (version temporaire)
Mean curvature flow is the gradient flow of the area functional and constitutes a natural geometric heat equation on the space of hypersurfaces in an ambient Riemannian manifold. It is believed, similar to Ricci Flow in the intrinsic setting, to have the potential to serve as a tool to app
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
The Most Difficult Math Problem You've Never Heard Of - Birch and Swinnerton-Dyer Conjecture
The Birch and Swinnerton-Dyer Conjecture is a millennium prize problem, one of the famed seven placed by the Clay Mathematical Institute in the year 2000. As the only number-theoretic problem in the list apart from the Riemann Hypothesis, the BSD Conjecture has been haunting mathematicians
From playlist Math
F. Schulze - Mean curvature flow with generic initial data
Mean curvature flow is the gradient flow of the area functional and constitutes a natural geometric heat equation on the space of hypersurfaces in an ambient Riemannian manifold. It is believed, similar to Ricci Flow in the intrinsic setting, to have the potential to serve as a tool to app
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics