The work of Martin Davis, Hilary Putnam, and Julia Robinson in 1961 completed by Yuri Matijasevic in 1970 proved that there is no general algorithm to decide whether a multivariable polynomial equation with integer coefficients has a solution in integers. It is still not known whether an algorithm exists for the analogous problem for rational numbers. I will describe progress on this and related problems.
Penn Mathematics Colloquium
Wednesday, October 3, 2007 - 4:30pm
Bjorn Poonen
UC Berkeley (visiting Harvard and MIT in Fall 2007)