School of Mathematical Sciences

From Schanuel's Conjecture to Shapiro's Conjecture menu

From Schanuel's Conjecture to Shapiro's Conjecture

Speaker: 
Angus Macintyre (QMUL)
Date/Time: 
Mon, 13/02/2012 - 16:30
Room: 
M103
Seminar series: 

Schanuel's Conjecture is a famous, and very powerful, conjecture about algebraic relations between complex numbers and their exponentials. Shapiro's Conjecture gives a necessary and sufficient conditin for two complex exponential polynomials to have infinitely many common zeros (this is a rare event). Montgomery gave an argument to show that this was not likely to yield to conventional approximation arguments from complex analysis. I sketch a proof that Schanuel implies Shapiro.