Ramanujan's master theorem

Daniel Spielman - Ramanujan Graphs and Free Probability

March 25, 2016 - This talk was part of the Minerva Lecture Series We use the method of interlacing polynomials and a finite dimensional analog of free probability to prove the existence of bipartite Ramanujan graphs of every degree and number of vertices. No prior knowledge of Ramanujan gr

From playlist Minerva Lectures - Daniel Spielman

Ramanujan graphs of every degree - Daniel Spielman

Daniel Spielman Yale University November 6, 2014 We explain what Ramanujan graphs are, and prove that there exist infinite families of bipartite Ramanujan graphs of every degree. Our proof follows a plan suggested by Bilu and Linial, and exploits a proof of a conjecture of theirs about li

From playlist Mathematics

Ramanujan: Making sense of 1+2+3+... = -1/12 and Co.

The Mathologer sets out to make sense of 1+2+3+ ... = -1/12 and some of those other notorious, crazy-looking infinite sum identities. The starting point for this video is the famous letter that led to the discovery of self-taught mathematical genius Srinivasa Ramanujan in 1913 (Ramanujan i

From playlist Recent videos

Winnie Li: Towers of Ramanujan graphs

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 Women at CIRM

Ramanujan's Pi Formula

The second video in a series about Ramanujan. Continuing the biography and a look at another of Ramanujan's formulas. This one involves Ramanujan's pi formula.

From playlist My Maths Videos

Ramanujan Graphs and Siran Graphs, Applications to Quantum Coding Theory - Jean-Pierre Tillich

Jean-Pierre Tillich INRIA, France March 16, 2012 We explain in this talk how Ramanujan graphs can be used to devise optimal cycle codes and review how other graph families related to a construction proposed by Margulis yield interesting families of quantum codes with logarithmic minimum di

From playlist Mathematics

Alexander Lubotzky - From Ramanujan graphs to Ramanujan complexes

December 17, 2014 - Analysis, Spectra, and Number theory: A conference in honor of Peter Sarnak on his 61st birthday. Ramanujan graphs has been defined and constructed in the 80's by Lubotzky-Phillips-Sarnak and by Margulis. In recent years a high dimensional theory of expanders is emer

From playlist Analysis, Spectra, and Number Theory - A Conference in Honor of Peter Sarnak on His 61st Birthday

Peter Sarnak - The Selberg Integral, Rankin Selberg Method, Arithmeticity [2008]

http://www.ams.org/notices/200906/rtx090600692p-corrected.pdf Saturday, January 12 12:00 PM Peter Sarnak The Selberg Integral, Rankin Selberg Method, Arithmeticity Atle Selberg Memorial Memorial Program in Honor of His Life & Work January 11-12, 2008 Renowned Norwegian mathematician A

From playlist Number Theory

Ramanujan Review

A sort of review of The Man Who Knew Infinity. And a *review* of other videos that came out this week. standupmaths: Ramanujan, 1729, Fermat's Last Theorem https://www.youtube.com/watch?v=_o0cIpLQApk Mathologer: Ramanujan. Making sense of -1/12 https://www.youtube.com/watch?v=jcKRGpMiVTw

From playlist My Maths Videos

The Generalized Ramanujan Conjectures and Applications (Lecture 2) by Peter Sarnak

Lecture 2: Thin Groups and Expansion Abstract: Infinite index subgroups of matrix groups like SL(n,Z) which are Zariski dense in SL(n), arise in many geometric and diophantine problems (eg as reflection groups,groups connected with elementary geometry such as integral apollonian packings,

From playlist Generalized Ramanujan Conjectures Applications by Peter Sarnak

"What is the Riemann Hypothesis and why does it matter?" by Ken Ono

The Riemann hypothesis provides insights into the distribution of prime numbers, stating that the nontrivial zeros of the Riemann zeta function have a “real part” of one-half. A proof of the hypothesis would be world news and fetch a $1 million Millennium Prize. In this lecture, Ken Ono wi

From playlist Number Theory Research Unit at CAMS - AUB

Number Theory, Symmetry and Zeta Functions - Peter Sarnak

75th Anniversary Celebration School of Mathematics Peter Sarnak Institute for Advanced Study March 11, 2005 More videos on http://video.ias.edu

From playlist Mathematics

Behind the Man Who Knew Infinity - Matthew Brown (director)

Stanford MRC co-hosted a presentation and panel discussion “Behind the Man Who Knew Infinity”, celebrating the life and work of Indian mathematician Ramanujan, on the occasion of the forthcoming film about him (starring Dev Patel and Jeremy Irons). The panel will feature Matthew Brown (dir

From playlist Mathematics Research Center

Niebur Integrals and Mock Automorphic Forms - Wladimir de Azevedo Pribitkin

Wladimir de Azevedo Pribitkin College of Staten Island, CUNY March 17, 2011 Among the bounty of brilliancies bequeathed to humanity by Srinivasa Ramanujan, the circle method and the notion of mock theta functions strike wonder and spark intrigue in number theorists fresh and seasoned alike

From playlist Mathematics

A Course of Pure Mathematics

In this video I will show you a legendary book that I have had for quite some time. This book was written by the famous G. H. Hardy who worked with Ramanujan in England. The book is titled A Course of Pure Mathematics. I hope you enjoy this video. Here it is https://amzn.to/3GBXKLc (this

From playlist Book Reviews

A New Proof of Bhramagupta’s Formula

For years John Conway searched for an elegant, symmetric, and geometric proof of Brahmagupta’s formula. Here it is, presented by a team of students from Proof School!

From playlist Summer of Math Exposition Youtube Videos

The Ramanujan Conjecture and some diophantine equations - Peter Sarnak

Speaker : Peter Sarnak Date and Time : Faculty Hall, IISc, Bangalore Venue : 25 May 12, 16:00 One of Ramanujan's most influential conjectures concerns the magnitude of the Fourier Coefficients of a modular form. These were made on the basis of his calculations as well as a far-reaching in

From playlist Public Lectures

Ramanujan's infinite root and its crazy cousins

In this video I'll talk about Ramanujan's infinite roots problem, give the solution to my infinite continued fraction puzzle from a couple of week's ago, and let you in on the tricks of the trade when it comes to making sense of all those crazy infinite expressions. Featuring guest appeara

From playlist Recent videos

Ramanujan Conjecture and the Density Hypothesis - Shai Evra

Joint IAS/Princeton University Number Theory Seminar Topic: Ramanujan Conjecture and the Density Hypothesis Speaker: Shai Evra Affiliation: Princeton University Date: November 19, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Ramanujan tau function and the Sato--Tate conjecture

From playlist Number Theory