# Seminar at SMU Delhi

November 21, 2012 (Wednesday) , 3:30 PM at Webinar
Speaker: Shanta Laishram, Indian Statistical Institute, Delhi
Title: Baker's Explicit ABC-Conjecture and Applications
Abstract of Talk
According to Nature News, 10 September 2012, a Japanese mathematician Shinichi Mochizuki claims to have proved "one of the most important unsolved problem in Diophantine Analysis, popularly known as \emph{abc conjecture} ". This conjecture of Masser-Oesterl\'e is a kind of grand unified theory of Diophantine Curves. This conjecture implies in a few lines the proofs of many difficult theorems and outstanding conjectures in Diophantine equations(including Fermat's Last Theorem). And once we have an explicit version of abc conjecture, we will be able to solve many of the conjectures completely. In a joint work with T. N. Shorey, we reformulate a explicit version due to Baker in the original form of abc conjecture and use it to solve a number of conjectures. In this talk, I will begin with introduction to abc conjecture with some motivation and history of this conjecture and talk about known results and our joint work. This talk will not include an introduction to the Inter-universal Teichm\H{u}ller Theory of Shinichi Mochizuki.