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
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
Recent progress in multiplicative number theory – Kaisa Matomäki & Maksym Radziwiłł – ICM2018
Number Theory Invited Lecture 3.5 Recent progress in multiplicative number theory Kaisa Matomäki & Maksym Radziwiłł Abstract: Multiplicative number theory aims to understand the ways in which integers factorize, and the distribution of integers with special multiplicative properties (suc
From playlist Number Theory
Number theory Full Course [A to Z]
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio
From playlist Number Theory
Christophe Soulé - 2/4 On the Arakelov theory of arithmetic
Let X be a semi-stable arithmetic surface of genus at least two and $\omega$ the relative dualizing sheaf of X, equipped with the Arakelov metric. Parshin and Moret-Bailly have conjectured an upper bound for the arithmetic self-intersection of $\omega$. They proved that a weak form of th
From playlist Christophe Soulé - On the Arakelov theory of arithmetic surfaces
Christophe Soulé - 1/4 On the Arakelov theory of arithmetic
Let X be a semi-stable arithmetic surface of genus at least two and $\omega$ the relative dualizing sheaf of X, equipped with the Arakelov metric. Parshin and Moret-Bailly have conjectured an upper bound for the arithmetic self-intersection of $\omega$. They proved that a weak form of th
From playlist Christophe Soulé - On the Arakelov theory of arithmetic surfaces
Christophe Soulé - 3/4 On the Arakelov theory of arithmetic
Let X be a semi-stable arithmetic surface of genus at least two and $\omega$ the relative dualizing sheaf of X, equipped with the Arakelov metric. Parshin and Moret-Bailly have conjectured an upper bound for the arithmetic self-intersection of $\omega$. They proved that a weak form of th
From playlist Christophe Soulé - On the Arakelov theory of arithmetic surfaces
Christophe Soulé - 4/4 On the Arakelov theory of arithmetic
Let X be a semi-stable arithmetic surface of genus at least two and $\omega$ the relative dualizing sheaf of X, equipped with the Arakelov metric. Parshin and Moret-Bailly have conjectured an upper bound for the arithmetic self-intersection of $\omega$. They proved that a weak form of th
From playlist Christophe Soulé - On the Arakelov theory of arithmetic surfaces
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
The GM-MDS conjecture - Shachar Lovett
More videos on http://video.ias.edu
From playlist Mathematics
Galois theory II | Math History | NJ Wildberger
We continue our historical introduction to the ideas of Galois and others on the fundamental problem of how to solve polynomial equations. In this video we focus on Galois' insights into how extending our field of coefficients, typically by introducing some radicals, the symmetries of the
From playlist MathHistory: A course in the History of Mathematics
Karl Schwede: Ordinary reductions & F singularities
In his seminal paper on arithmetic surfaces Faltings introduced a new invariant associated to compact Riemann surfaces. For a given compact Riemann surface X of genus g, this invariant is roughly given as minus the logarithm of the distance of the point in the moduli space of genus g curve
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Bourbaki - 07/11/15 - 3/4 - Benoît CLAUDON
Semi-positivité du cotangent logarithmique et conjecture de Shafarevich-Viehweg, d’après Campana, Pa ̆un, Taji,... Démontrée par A. Parshin et S. Arakelov au début des années 1970, la conjecture d’hyperbolicité de Shafarevich affirme qu’une famille de courbes de genre g ≥ 2 paramétrée pa
From playlist Bourbaki - 07 novembre 2015
Andrew Wiles | Twenty Years of Number Theory | 1998
Notes for this talk: https://drive.google.com/file/d/1eJXPwL772Z00egvLjO3VHmvCv7mwcv6Q/view?usp=sharing Twenty Years of Number Theory Andrew Wiles Princeton University ICM Berlin 19.08.1998 https://www.mathunion.org/icm/icm-videos/icm-1998-videos-berlin-germany/icm-berlin-videos-2708
From playlist Number Theory
Alan Turing and Number Theory - Yuri Matiyasevich (St. Petersburg) [2012]
slides for this talk: http://videolectures.net/site/normal_dl/tag=694395/turing100_matiyasevich_number_theory_01.pdf Alan Turing Centenary Conference Manchester, 2012 Alan Turing and Number Theory Yuri Matiyasevich, St.Petersburg Department of Steklov Mathematical Institute, Russian Aca
From playlist Mathematics
In this video, we explore the "pattern" to prime numbers. I go over the Euler product formula, the prime number theorem and the connection between the Riemann zeta function and primes. Here's a video on a similar topic by Numberphile if you're interested: https://youtu.be/uvMGZb0Suyc The
From playlist Other Math Videos
Electrical Engineering: Ch 12 AC Power (52 of 58) Power Factor Correction: Example Part 3
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the changes of the phase angle, phi, by substituting the capacitor required of 2, 4, 6,8, and 20 ohms. (Part 3) To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?
From playlist ELECTRICAL ENGINEERING 12 AC POWER
Physics 37.1 Gauss's Law Understood (22 of 29) Infinite Sheet of Charge
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the electric field E=? a distance from an infinite sheet of charge where the area charge density is given. Next video in this series can be seen at: https://youtu.be/ZKlK-AMOtAU
From playlist PHYSICS 37.1 GAUSS'S LAW EXPLAINED
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
Astronomy - Ch. 10: Mercury (10 of 42) What Determines if a Planet will have an Atmosphere?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the three (2 main) factors determining if a planet has an atmosphere. The 2 main factors are 1) temperature (affects the speed of the molecules in the atmosphere.), 2) gravity (affects the “pu
From playlist ASTRONOMY 10 MERCURY