Conjectures that have been proved | Surfaces | Theorems in differential geometry
In differential geometry, the Willmore conjecture is a lower bound on the Willmore energy of a torus. It is named after the English mathematician Tom Willmore, who conjectured it in 1965. A proof by Fernando Codá Marques and André Neves was announced in 2012 and published in 2014. (Wikipedia).
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
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
D. Ketover - Sharp entropy bounds of closed surfaces and min-max theory
In 2012, Colding-Ilmanen-Minicozzi-White conjectured that the entropy of any closed surface in R^3 is at least that of the self-shrinking two-sphere. I will explain joint work with X. Zhou where we interpret this conjecture as a parabolic version of the Willmore problem and give a min-max
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
Convolution Theorem: Fourier Transforms
Free ebook https://bookboon.com/en/partial-differential-equations-ebook Statement and proof of the convolution theorem for Fourier transforms. Such ideas are very important in the solution of partial differential equations.
From playlist Partial differential equations
C73 Introducing the theorem of Frobenius
The theorem of Frobenius allows us to calculate a solution around a regular singular point.
From playlist Differential Equations
Morse-Theoretic Aspects of the Willmore Energy - Alexis Michelat
Variational Methods in Geometry Seminar Topic: Morse-Theoretic Aspects of the Willmore Energy Speaker: Alexis Michelat Affiliation: ETH Zurich Date: November 13, 2018 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Solve a Bernoulli Differential Equation (Part 2)
This video provides an example of how to solve an Bernoulli Differential Equation. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
Huy Nguyen: Brakke Regularity for the Allen-Cahn Flow
Abstract: In this paper we prove an analogue of the Brakke's $\epsilon$-regularity theorem for the parabolic Allen--Cahn equation. In particular, we show uniform $C^{2,\alpha}$ regularity for the transition layers converging to smooth mean curvature flows as $\epsilon\rightarrow 0$. A corr
From playlist MATRIX-SMRI Symposium: Singularities in Geometric Flows
This is one of my all-time favorite differential equation videos!!! :D Here I'm actually using the Wronskian to actually find a nontrivial solution to a second-order differential equation. This is amazing because it brings the concept of the Wronskian back to life! And as they say, you won
From playlist Differential equations
Henri Darmon: Andrew Wiles' marvelous proof
Abstract: Pierre de Fermat famously claimed to have discovered “a truly marvelous proof” of his last theorem, which the margin in his copy of Diophantus' Arithmetica was too narrow to contain. Fermat's proof (if it ever existed!) is probably lost to posterity forever, while Andrew Wiles' p
From playlist Abel Lectures
Albert Einstein, Holograms and Quantum Gravity
In the latest campaign to reconcile Einstein’s theory of gravity with quantum mechanics, many physicists are studying how a higher dimensional space that includes gravity arises like a hologram from a lower dimensional particle theory. Read about the second episode of the new season here:
From playlist In Theory
Andrew Wiles: Fermat's Last theorem: abelian and non-abelian approaches
The successful approach to solving Fermat's problem reflects a move in number theory from abelian to non-abelian arithmetic. This lecture was held by Abel Laurate Sir Andrew Wiles at The University of Oslo, May 25, 2016 and was part of the Abel Prize Lectures in connection with the Abel P
From playlist Sir Andrew J. Wiles
Emmanuel Maitre: Diffusion redistanciation schemes, Willmore problem and red blood cells
Recording during the thematic meeting : "CEMRACS : Numerical and Mathematical Modeling for Biological and Medical Applications : Deterministic, Probabilistic and Statistical Descriptions" the August 03, 2018 at the Centre International de Rencontres Mathématiques (Marseille, France) Film
From playlist Numerical Analysis and Scientific Computing
In visual computing, point locations are often optimized using a "repulsive" energy, to obtain a nice uniform distribution for tasks ranging from image stippling to mesh generation to fluid simulation. But how do you perform this same kind of repulsive optimization on curves and surfaces?
From playlist Repulsive Videos
Recent developments in non-commutative Iwasawa theory I - David Burns
David Burns March 25, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Solve a Bernoulli Differential Equation (Part 1)
This video provides an example of how to solve an Bernoulli Differential Equation. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
Giles Gardam: Kaplansky's conjectures
Talk by Giles Gardam in the Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/3580/ on September 17, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Giles Gardam - Kaplansky's conjectures
Kaplansky made various related conjectures about group rings, especially for torsion-free groups. For example, the zero divisors conjecture predicts that if K is a field and G is a torsion-free group, then the group ring K[G] has no zero divisors. I will survey what is known about the conj
From playlist Talks of Mathematics Münster's reseachers
A (compelling?) reason for the Riemann Hypothesis to be true #SOME2
A visual walkthrough of the Riemann Zeta function and a claim of a good reason for the truth of the Riemann Hypothesis. This is not a formal proof but I believe the line of argument could lead to a formal proof.
From playlist Summer of Math Exposition 2 videos