Attività del Dipartimento

Colloquium di Matematica

On the abc Conjecture and some of its consequences

Michel Waldschmidt

14-11-2023 - 16:15
Largo Lungo Tevere Dante n 376 - Aula M1


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.
org: BARROERO Fabrizio