Colloquium di Matematica: On the abc Conjecture and some of its consequences

Martedì 14 novembre alle ore 16:15, Michel Waldschmidt (Sorbonne University Institut Mathématique de Jussieu), terrà il Colloquium di Matematica dal titolo "On the abc Conjecture and some of its consequences".

Abstract:
According to Nature News, 10 September 2012, quoting Dorian Goldfeld, the abc Conjecture is “the most important unsolved problem in Diophantine analysis”. It is a kind of grand unified theory of Diophantine curves : “The remarkable thing about the abc Conjecture is that it provides a way of reformulating an infinite number of Diophantine problems,” says Goldfeld, “and, if it is true, of solving them.” Proposed independently in the mid-80s by David Masser of the University of Basel and Joseph Oesterlé of Pierre et Marie Curie University (Paris 6), the abc Conjecture describes a kind of balance or tension between addition and multiplication, formalizing the observation that when two numbers a and b are divisible by large powers of small primes,
a + b tends to be divisible by small powers of large primes. The abc Conjecture implies – in a few lines – the proofs of many difficult theorems and outstanding conjectures in Diophantine equations– including Fermat’s Last Theorem.

This talk will be at an elementary level, giving a collection of consequences of the abc Conjecture. It will not include an introduction to the Inter-universal Teichmüller Theory of Shinichi Mochizuki.

Il seminario avrà luogo in presenza presso il Dipartimento di Matematica e Fisica, Lungotevere Dante, 376 - Aula M1.