the $s$-unit equation has vast applications in number theory. we will discuss an implementation of an algorithm to solve the $s$-unit equation in the mathematical software sage.  the mathematical foundation for this implementation and some applications will be outlined, including an asymptotic version of fermat's last theorem for totally real cubic number fields with bounded discriminant in which 2 is totally ramified. we will conclude with a discussion on current and future work toward improving the existing sage functionality.

[pre-talk at 1:20pm, in person only]