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
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
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
Yitang Zhang and The Landau-Siegel Zero Problem in Number Theory [2019] (in Chinese)
Abstract: As a special and (probably) much weaker form of the Generalized Riemann Hypothesis, the Landau-Siegel zero problem has its own interest and amazing applications in number theory. In this talk we will introduce its history and applications. In particular, it will be explained why
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
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
Sir Michael Atiyah | The Riemann Hypothesis | 2018
Slides for this talk: https://drive.google.com/file/d/1DNHG9TDXiVslO-oqDud9f-9JzaFCrHxl/view?usp=sharing Sir Michael Francis Atiyah: "The Riemann Hypothesis" Monday September 24, 2018 9:45 Abstract: The Riemann Hypothesis is a famous unsolved problem dating from 1859. I will present a
From playlist Number Theory
Gonçalo Tabuada - 1/3 Noncommutative Counterparts of Celebrated Conjectures
Some celebrated conjectures of Beilinson, Grothendieck, Kimura, Tate, Voevodsky, Weil, and others, play a key central role in algebraic geometry. Notwithstanding the effort of several generations of mathematicians, the proof of (the majority of) these conjectures remains illusive. The aim
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
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
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
Terence Tao (UCLA): Pseudorandomness of the Liouville function
The Liouville pseudorandomness principle (a close cousin of the Mobius pseudorandomness principle) asserts that the Liouville function λ(n), which is the completely multiplicative function that equals −1 at every prime, should be "pseudorandom" in the sense that it behaves statistically li
From playlist TP Harmonic Analysis and Analytic Number Theory: Opening Day
Ciprian Demeter (Bloomington): Restriction of exponential sums to hypersurfaces
We discuss moment inequalities for exponential sums with respect to singular measures, whose Fourier decay matches those of curved hypersurfaces. Our emphasis will be on proving estimates that are sharp with respect to the scale parameter N apart from Nϵ losses. Joint work with Bartosz Lan
From playlist Seminar Series "Harmonic Analysis from the Edge"
Gonçalo Tabuada - 3/3 Noncommutative Counterparts of Celebrated Conjectures
Some celebrated conjectures of Beilinson, Grothendieck, Kimura, Tate, Voevodsky, Weil, and others, play a key central role in algebraic geometry. Notwithstanding the effort of several generations of mathematicians, the proof of (the majority of) these conjectures remains illusive. The aim
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Eric Urban - Relations entières de périodes pour le changement de base
L’étude des congruences entre un changement de base d’une forme modulaire elliptique à une extension quadratique F/Q avec des formes qui n’en sont pas est étroitement liée aux relations entières entre les périodes du changement de base et celles de la forme de
From playlist Reductive groups and automorphic forms. Dedicated to the French school of automorphic forms and in memory of Roger Godement.
[BOURBAKI 2018] 13/01/2018 - 2/4 - Raphaël BEUZART-PLESSIS
Progrès récents sur les conjectures de Gan-Gross-Prasad [d'après Jacquet-Rallis, Waldspurger, W. Zhang, etc.] Les conjectures de Gan-Gross-Prasad ont deux aspects: localement elles décrivent de façon explicite certaines lois de branchements entre représentations de groupes de Lie réels ou
From playlist BOURBAKI - 2018
The Million Dollar Problem that Went Unsolved for a Century - The Poincaré Conjecture
Topology was barely born in the late 19th century, but that didn't stop Henri Poincaré from making what is essentially the first conjecture ever in the subject. And it wasn't any ordinary conjecture - it took a hundred years of mathematical development to solve it using ideas so novel that
From playlist Math
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
Understanding and computing the Riemann zeta function
In this video I explain Riemann's zeta function and the Riemann hypothesis. I also implement and algorithm to compute the return values - here's the Python script:https://gist.github.com/Nikolaj-K/996dba1ff1045d767b10d4d07b1b032f
From playlist Programming