Mertens Conjecture Disproof and the Riemann Hypothesis | MegaFavNumbers
#MegaFavNumbers The Mertens conjecture is a conjecture is a conjecture about the distribution of the prime numbers. It can be seen as a stronger version of the Riemann hypothesis. It says that the Mertens function is bounded by sqrt(n). The Riemann hypothesis on the other hand only require
From playlist MegaFavNumbers
Here I prove the Heine-Borel Theorem, one of the most fundamental theorems in analysis. It says that in R^n, all boxes must be compact. The proof itself is very neat, and uses a bisection-type argument. Enjoy! Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHG
From playlist Topology
Bruno Klingler - 3/4 Tame Geometry and Hodge Theory
Hodge theory, as developed by Deligne and Griffiths, is the main tool for analyzing the geometry and arithmetic of complex algebraic varieties. It is an essential fact that at heart, Hodge theory is NOT algebraic. On the other hand, according to both the Hodge conjecture and the Grothendie
From playlist Bruno Klingler - Tame Geometry and Hodge Theory
Bruno Klingler - 2/4 Tame Geometry and Hodge Theory
Hodge theory, as developed by Deligne and Griffiths, is the main tool for analyzing the geometry and arithmetic of complex algebraic varieties. It is an essential fact that at heart, Hodge theory is NOT algebraic. On the other hand, according to both the Hodge conjecture and the Grothendie
From playlist Bruno Klingler - Tame Geometry and Hodge Theory
Bruno Klingler - 4/4 Tame Geometry and Hodge Theory
Hodge theory, as developed by Deligne and Griffiths, is the main tool for analyzing the geometry and arithmetic of complex algebraic varieties. It is an essential fact that at heart, Hodge theory is NOT algebraic. On the other hand, according to both the Hodge conjecture and the Grothendie
From playlist Bruno Klingler - Tame Geometry and Hodge Theory
Existence & Uniqueness Theorem, Ex1.5
Existence & Uniqueness Theorem for differential equations. Subscribe for more math for fun videos 👉 https://bit.ly/3o2fMNo For more calculus & differential equation tutorials, check out @justcalculus 👉 https://www.youtube.com/justcalculus To learn how to solve different types of d
From playlist Differential Equations: Existence & Uniqueness Theorem (Nagle Sect1.2)
Étale cohomology Lecture II, 8/25/2020
Serre's complex analogue of the Riemann hypothesis, Ă©tale morphisms, intro to sites
From playlist Étale cohomology and the Weil conjectures
Ian Agol, Lecture 3: Applications of Kleinian Groups to 3-Manifold Topology
24th Workshop in Geometric Topology, Calvin College, June 30, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
F. Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 1)
The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics. - The Andreev-Koebe-Thurston theorem on circle packing polyhedral metrics and Marden-Rodin’s proof - Thurston’s conjecture o
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
F. Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 3)
The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics. - The Andreev-Koebe-Thurston theorem on circle packing polyhedral metrics and Marden-Rodin’s proof - Thurston’s conjecture o
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
F. Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 5)
The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics. - The Andreev-Koebe-Thurston theorem on circle packing polyhedral metrics and Marden-Rodin’s proof - Thurston’s conjecture o
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
F. Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 2)
The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics. - The Andreev-Koebe-Thurston theorem on circle packing polyhedral metrics and Marden-Rodin’s proof - Thurston’s conjecture o
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
F. Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 4)
The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics. - The Andreev-Koebe-Thurston theorem on circle packing polyhedral metrics and Marden-Rodin’s proof - Thurston’s conjecture o
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
Models for Galois deformation rings - Brandon Levin
Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program Topic: Models for Galois deformation rings Speaker: Brandon Levin Affiliation: University of Chicago Date: November 9, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Ariyan Javanpeykar: Arithmetic and algebraic hyperbolicity
Abstract: The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of “rational points”. For instance, it suggests a striking answer to the fundamental question “Why do some polynomial equations with integer coefficients have onl
From playlist Algebraic and Complex Geometry
Monodromy Theorem, Weight Filtration, Weight-Monodromy Theorem
We state Scholze's Theorem and some of the theorems around them. This will be applied later.
From playlist Hodge Theory
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
Bruno Klingler - 1/4 Tame Geometry and Hodge Theory
Sorry for the re upload due to a technical problem on the previous version Hodge theory, as developed by Deligne and Griffiths, is the main tool for analyzing the geometry and arithmetic of complex algebraic varieties. It is an essential fact that at heart, Hodge theory is NOT algebraic.
From playlist Bruno Klingler - Tame Geometry and Hodge Theory
Ryan Kinser - Module varieties with dense orbits in every component
Research lecture at the Worldwide Center of Mathematics
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS
The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t
From playlist Introduction to Homotopy Theory