Maxson Lecture Series

Date: April 21, 2014

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Bjorn Poonen, MIT

Title: Undecidability in number theory

Abstract: Hilbert's Tenth Problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients, would decide whether there exists a solution in integers. Around 1970, Matiyasevich, building on earlier work of Davis, Putnam, and Robinson, showed that no such algorithm exists. But the answer to the analogous question with integers replaced by rational numbers is still unknown, and there is not even agreement among experts as to what the answer should be.