Undecidability of polynomial equations over C(t_1,t_2)

abstract:
In 1992 Kim and Roush used Matiyasevich's negative answer to Hilbert's 10th
problem to prove that there is no general algorithm for deciding whether a
multivariable polynomial equation with coefficients in $\mathbb{C}(t_1,t_2)$
has a solution in that field.  We give an exposition of this theorem
and related results and open problems.