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
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
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
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
Shou-Wu Zhang: Congruent number problem and BSD conjecture
Abstract : A thousand years old problem is to determine when a square free integer n is a congruent number ,i,e, the areas of right angled triangles with sides of rational lengths. This problem has a some beautiful connection with the BSD conjecture for elliptic curves En:ny2=x3−x. In fact
From playlist Jean-Morlet Chair - Research Talks - Prasad/Heiermann
John Pardon: Totally disconnected groups (not) acting on three-manifolds
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Geometry
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
The Hecke category action on the principal block via Smith theory - Geordie Williamson
Geometric and Modular Representation Theory Seminar Topic: The Hecke category action on the principal block via Smith theory Speaker: Geordie Williamson Affiliation: University of Sydney; Distinguished Visiting Professor, School of Mathematics Date: January 27, 2021 For more video please
From playlist Geordie Williamson external seminars
Number Theory | A very special case of Fermat's Last Theorem
We prove a very simple case of Fermat's Last Theorem. Interestingly, this case is fairly easy to prove which highlights the allure of the theorem as a whole -- especially given the fact that much of modern number theory was developed as part of the program that ended in the full proof. ht
From playlist Number Theory
Geordie Williamson: Miraculous Treumann-Smith theory and geometric Satake
Abstract: This talk will be about geometric approaches to the representation theory of reductive algebraic groups in positive characteristic p. A cornerstone of the geometric theory is the geometric Satake equivalence, which gives an incarnation of the category of representations as a cate
From playlist Geordie Williamson: Representation theory and the Geometric Satake
Mateusz Michalek: "Algebraic methods to construct tensors"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop III: Mathematical Foundations and Algorithms for Tensor Computations "Algebraic methods to construct tensors" Mateusz Michalek - Universität Konstanz, Institute of Mathematics Abstract: We will prese
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
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
Geordie Williamson: Parity sheaves and modular representations II
This is a talk of Gordie Williamson given at the Harvard CDM Conference of November 23, 2019.
From playlist Geordie Williamson: Parity sheaves and modular representations
New Age Linkage - Daniel Juteau
Geometric and Modular Representation Theory Seminar Topic: New Age Linkage Speaker: Daniel Juteau Affiliation: CNRS, Université Paris Diderot; Member, School of Mathematics Date: January 20, 2021 For more video please visit http://video.ias.edu
From playlist Seminar on Geometric and Modular Representation Theory
Smith theory and Langlands functoriality - Tony Feng
Workshop on Representation Theory and Geometry Topic: Smith theory and Langlands functoriality Speaker: Tony Feng Affiliation: Member, School of Mathematics Date: March 29, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Xin Zhou - Recent developments in constant mean curvature hypersurfaces I
We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well. Xin Zhou (Cornell)
From playlist Not Only Scalar Curvature Seminar
2^k-Selmer groups and Goldfeld's conjecture. - Smith - Workshop 2 - CEB T2 2019
Alexander Smith (Harvard University) / 25.06.2019 2^k-Selmer groups and Goldfeld's conjecture. Take E to be an elliptic curve over a number field whose four torsion obeys certain technical conditions. In this talk, we will outline a proof that 100% of the quadratic twists of E have rank
From playlist 2019 - T2 - Reinventing rational points
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