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
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
ABC Intro - part 1 - What is the ABC conjecture?
This videos gives the basic statement of the ABC conjecture. It also gives some of the consequences.
From playlist ABC Conjecture Introduction
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
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
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
Harold Stark - The origins of conjectures on derivatives of L-functions at s=0 [1990’s]
slides for this talk: http://www.msri.org/realvideo/ln/msri/2001/rankin-L/stark/1/banner/01.html The origins of conjectures on derivatives of L-functions at s=0 Harold Stark http://www.msri.org/realvideo/ln/msri/2001/rankin-L/stark/1/index.html
From playlist Number Theory
The Zilber-Pink conjecture - Jonathan Pila
Hermann Weyl Lectures Topic: The Zilber-Pink conjecture Speaker: Jonathan Pila Affiliation: University of Oxford Date: October 26, 2018 For more video please visit http://video.ias.edu
From playlist Hermann Weyl Lectures
What is the Lang-Bombieri-Noguchi Conjecture?
Here we introduce the conjecture of Lang, Bombieri and Noguchi about the density rational points on varieties of general type.
From playlist One-off Explanations
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
Stephanie Chan, Integral points in families of elliptic curves
VaNTAGe Seminar, June 28, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk: Hindry-Silverman: https://eudml.org/doc/143604 Alpoge: https://arxiv.org/abs/1412.1047 Bhargava-Shankar: https://arxiv.org/abs/1312.7859 Brumer-McGuiness: https://www.ams.org/journal
From playlist Arithmetic Statistics II
Spectra of metric graphs and crystalline measures - Peter Sarnak
Members' Seminar Topic: Spectra of metric graphs and crystalline measures Speaker: Peter Sarnak Affiliation: Professor, School of Mathematics Date: February 10, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Point-counting and diophantine applications - Jonathan Pila
Hermann Weyl Lectures Topic: Point-counting and diophantine applications Speaker: Jonathan Pila Affiliation: University of Oxford Date: October 23, 2018 For more video please visit http://video.ias.edu
From playlist Hermann Weyl Lectures
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
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
Youness Lamzouri: Large character sums
Abstract : For a non-principal Dirichlet character χ modulo q, the classical Pólya-Vinogradov inequality asserts that M(χ):=maxx|∑n≤xχ(n)|=O(q‾√log q). This was improved to q‾√log log q by Montgomery and Vaughan, assuming the Generalized Riemann hypothesis GRH. For quadratic characters, th
From playlist Number Theory
What is the Mordell-Lang problem?
It is my intention to eventually explain some things about the Mordell-Lang problem and the higher dimensional versions of these. The presentation in this video is due to Mazur and can be found in an MSRI article he wrote that introduces these things.
From playlist Mordell-Lang
Eric Riedl: A Grassmannian technique and the Kobayashi Conjecture
Abstract: An entire curve on a complex variety is a holomorphic map from the complex numbers to the variety. We discuss two well-known conjectures on entire curves on very general high-degree hypersurfaces X in ℙn: the Green-Griffiths-Lang Conjecture, which says that the entire curves lie
From playlist Algebraic and Complex Geometry
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