Mertens conjecture

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

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

Riemann Series Theorem

In this video, I explain a quite unbelievable fact about series: If a series converges, but does not converge absolutely, then we can rearrange it to have any limit that we want! Enjoy this beautiful analysis extravaganza, also known as the Riemann Rearrangement Theorem. Rearrange a serie

From playlist Series

A Prime Surprise (Mertens Conjecture) - Numberphile

Dr Holly Krieger discusses Merterns' Conjecture. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More videos with Holly (playlist): http://bit.ly/HollyKrieger Dr Holly Krieger is the C

From playlist Women in Mathematics - Numberphile

Theory of numbers: Fermat's theorem

This lecture is part of an online undergraduate course on the theory of numbers. We prove Fermat's theorem a^p = a mod p. We then define the order of a number mod p and use Fermat's theorem to show the order of a divides p-1. We apply this to testing some Fermat and Mersenne numbers to se

From playlist Theory of numbers

Heine Borel Theorem

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

An Amazing Connection Between the Riemann Hypothesis and Topology

https://gregoriousmaths.com/2021/08/19/a-couple-of-other-connections-between-number-theory-and-topology/ 0:00 Introduction and plan 2:32 The Riemann hypothesis 7:22 Introducing the complex we will study 19:41 Studying the asymptotic behaviour of \beta_k(\Delta_n) 22:54 Some number theoret

From playlist Summer of Math Exposition Youtube Videos

Weil conjectures 4 Fermat hypersurfaces

This talk is part of a series on the Weil conjectures. We give a summary of Weil's paper where he introduced the Weil conjectures by calculating the zeta function of a Fermat hypersurface. We give an overview of how Weil expressed the number of points of a variety in terms of Gauss sums. T

From playlist Algebraic geometry: extra topics

Maximum modulus principle

Maximum modulus principle In this video, I talk about the maximum modulus principle, which says that the maximum of the modulus of a complex function is attained on the boundary. I also show that the same thing is true for the real and imaginary parts, and finally I discuss the strong max

From playlist Complex Analysis

Primes, Complexity and Computation: How Big Number theory resolves the Goldbach Conjecture

This lecture, which begins at 2:45, shows how Big Number theory, together with an understanding of prime numbers and their distribution resolves the Goldbach Conjecture, which states that every even number greater than two is the sum of two primes. Notions of complexity and computation,

From playlist MathSeminars

Risk Management Lesson 8A: Industrial Models for Credit Risk

In this first part of Lesson 8, we deal with two important credit risk models developed by the industry. Topics: - Moody's KMV - CreditMetrics (J.P. Morgan & Co.)

From playlist Risk Management

The Selberg sieve (Lecture 1) by Stephan Baier

Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod

From playlist Workshop on Additive Combinatorics 2020

The hyperbolic Ax-Lindemann conjecture - Emmanuel Ullmo

Emmanuel Ullmo Université Paris-Sud February 7, 2014 The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort

From playlist Mathematics

Stokes Theorem

In this video, I present another example of Stokes theorem, this time using it to calculate the line integral of a vector field. It is a very useful theorem that arises a lot in physics, for example in Maxwell's equations. Other Stokes Example: https://youtu.be/-fYbBSiqvUw Yet another Sto

From playlist Vector Calculus

Limit Theorems for the Möbius function Function and Statistical Mechanics - Francesco Cellarosi

Francesco Cellarosi Princeton University March 29, 2011 I will present a recent joint work with Ya.G. Sinai. We investigate the ``randomness" of the classical Möbius function by means of a statistical mechanical model for square-free numbers and we prove some new results, including a non-s

From playlist Mathematics

Large deviation estimates for Selberg’s central limit theorem, applications, and..... - Emma Bailey

50 Years of Number Theory and Random Matrix Theory Conference Large deviation estimates for Selberg’s central limit theorem, applications, and numerics Speaker: Emma Bailey Affiliation: City University of New York June 22, 2022 Selberg’s celebrated central limit theorem shows that the lo

From playlist Mathematics

Liouville and JT Quantum Gravity - Holography and Matrix Models - Thomas Mertens

Online Workshop on Qubits and Black Holes Topic: Liouville and JT Quantum Gravity - Holography and Matrix Models Thomas Mertens Ghent University Date: December 8, 2020 For more video please visit http://video.ias.edu

From playlist Natural Sciences

The Fyodorov-Hiary-Keating Conjecture - Louis-Pierre Arguin

50 Years of Number Theory and Random Matrix Theory Conference Topic: The Fyodorov-Hiary-Keating Conjecture Speaker: Louis-Pierre Arguin Affiliation: City University of New York June 22, 2022 In 2012, Fyodorov, Hiary & Keating and Fyodorov & Keating proposed a series of conjectures descri

From playlist Mathematics

Zermelo Fraenkel Introduction

This lecture is part of an online course on the Zermelo Fraenkel axioms of set theory. This lecture gives an overview of the axioms, describes the von Neumann hierarchy, and sketches several approaches to interpreting the axioms (Platonism, von Neumann hierarchy, multiverse, formalism, pra

From playlist Zermelo Fraenkel axioms