The Tau of Ramanujan by Eknath Ghate

Explore the fascinating world of Ramanujan's tau-function in this captivating lecture by Eknath Ghate. Delve into the sequence of numbers 1, -24, 252, -1472, 4830, and beyond, which have been a driving force in Number Theory for nearly a century. Discover how these intriguing numbers continue to challenge mathematicians with easily understood yet unsolved problems. Journey through various mathematical concepts, including Math Circles, Euler's work, patterns, Wyler's Theorem, partitions, and the famous Gauss story. Learn about modular forms, Galois theory, group theory, and their connections to Ramanujan's tau-function. Gain insights into the significance of the Fields Medal and explore the aesthetic appeal of mathematics. This comprehensive talk, presented at the J. N. Planetarium in Bangalore, offers a relaxed introduction to Ramanujan's tau-function and showcases some of the speaker's own findings on this captivating mathematical subject.

Introduction
Math Circle
Introducing Professor Todd Carter
What is Mathematics
Challenging
Aesthetics
Mathematics
Oyler
Patterns
Wylers Theorem
Partitions
Gauss Story
Cancellations
ROM Origin
Taxi Story
Back to Tau
Modular Forms
Galois
Galois Theory
Group Theory
Galois representations
Tower values
Sigma11 function
oneline proof
Eisenstein series
Fields Medal
Problem