Analytic number theory

Factorials, prime numbers, and the Riemann Hypothesis

Today we introduce some of the ideas of analytic number theory, and employ them to help us understand the size of n!. We use that understanding to discover a surprisingly accurate picture of the distribution of the prime numbers, and explore how this fits into the broader context of one o

From playlist Analytic Number Theory

Analytic Number Theory with Sage - Kamalakshya Mehatab

Video taken from: http://ekalavya.imsc.res.in/node/451

From playlist Mathematics

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

The Prime Number Theorem, an introduction ← Number Theory

An introduction to the meaning and history of the prime number theorem - a fundamental result from analytic number theory. Narrated by Cissy Jones Artwork by Kim Parkhurst, Katrina de Dios and Olga Reukova Written & Produced by Michael Harrison & Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ Ways t

From playlist Number Theory

Analytic Continuation and the Zeta Function

Where do complex functions come from? In this video we explore the idea of analytic continuation, a powerful technique which allows us to extend functions such as sin(x) from the real numbers into the complex plane. Using analytic continuation we can finally define the zeta function for co

From playlist Analytic Number Theory

Theory of numbers: Multiplicative functions

This lecture is part of an online undergraduate course on the theory of numbers. Multiplicative functions are functions such that f(mn)=f(m)f(n) whenever m and n are coprime. We discuss some examples, such as the number of divisors, the sum of the divisors, and Euler's totient function.

From playlist Theory of numbers

What is... an elliptic curve?

In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were

From playlist An Introduction to the Arithmetic of Elliptic Curves

Terence Tao: The circle method from the perspective of higher order Fourier analysis

Higher order Fourier analysis is a collection of results and methods that can be used to control multilinear averages (such as counts for the number of four-term progressions in a set) that are out of reach of conventional linear Fourier analysis methods (i.e., out of reach of the circle m

From playlist Harmonic Analysis and Analytic Number Theory

Boris Adamczewski 04/27/18

Mahler's method: old and new

From playlist Spring 2018

Robert Langlands - "The Elephant" [2001]

Conference on Automorphic Forms: Concepts, Techniques, Applications and Influence April 4, 2001 - April 7, 2001 https://video.ias.edu/Automorphic-Forms

From playlist Number Theory

Marco Serone - 1/3 Resurgence in Integrable Field Theories

: We review recent progress in understanding the resurgent properties of integrable field theories in two dimensions. After a brief recap on elementary notions about Borel resummations, we start with a quick historical detour on the study of the large order behaviour of perturbation theory

From playlist Marco Serone - Resurgence in Integrable Field Theories

The Hybrid Conformal Bootstrap by Ning Su

NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (IISER Mohal

From playlist NUMSTRING 2022

James Freitag, University of Illinois at Chicago

March 29, James Freitag, University of Illinois at Chicago Not Pfaffian

From playlist Spring 2022 Online Kolchin seminar in Differential Algebra

A search for an algebraic equivalence analogue of motivic theories - Eric Friedlander

Vladimir Voevodsky Memorial Conference Topic: A search for an algebraic equivalence analogue of motivic theories Speaker: Eric Friedlander Affiliation: University of Southern California Date: September 13, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

Complex Langevin Dynamics in Large-N Gauge Theories by Pallab Basu

Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to

From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography

Two Applications of the Bootstrap in QCD (Lecture 2) by Martin Kruczenski

PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II

From playlist NUMSTRING 2022

Tame topologies in non-archimedean geometry - Abhishek Oswal

Short Talks by Postdoctoral Members Topic: Tame topologies in non-archimedean geometry Speaker: Abhishek Oswal Affiliation: Member, School of Mathematics Date: September 25, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Sidney Coleman lecture 43

From playlist Full course: Quantum Field Theory by Sidney Coleman (1975) [Havard Physics 253]

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

Marco SERONE - A look at \phi^4_2 using perturbation theory

https://indico.math.cnrs.fr/event/2435/

From playlist Workshop “Hamiltonian methods in strongly coupled Quantum Field Theory”