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Seminars and Colloquia

Mathematics

On the $abc$ conjecture and some of its consequences  
 
Fri, Nov 24, 2017,   04:30 PM to 05:30 PM at Madhava Hall

Prof. Michel Waldschmidt
University of Paris VI

According to http://www.ams.org/news/math-in-the-media/mathdigest-index%#201210-numbers 
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. 
 

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