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

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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".

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.