Theoretical Statistics and Mathematics Unit, ISI 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.