COLLOQUIO DE GIORGI Yuri Bilu Universitè de Bordeaux I "Diophantine equations with separated variables" We describe pairs (f,g) of polynomials with rational coefficients such that the equation f(x)=g(y) has infinitely many solutions in integers x,y. Using classical results of Siegel and Ritt, together with some ideas of M. Fried, we show that, up to a linear change of variables, any such pair is of the form f(x) = h(u(x)) and g(y) = h(v(y)), where u,v are polynomials of very particular form and h is an arbitrary polynomial with rational coefficients. Martedì 21 febbraio 2006 ore 17.00 Aula Mancini Piazza dei Cavalieri, 7 PISA _______________________________________________ Settimanale mailing list Settimanale@mail.dm.unipi.it https://mail.dm.unipi.it/mailman/listinfo/settimanale