It seems as though the SIAM class does not play nice with the cases environment. For example
$$
\begin{cases}
x & y
\end{cases}
$$
will produce the error
misplaced alignment tab character
Oddly enough,
$$
\begin{cases}
x \\ y
\end{cases}
$$
compiles, but puts x and y on the same line.
cases
environment is defined inamsmath
so you presumably want\usepackage{amsmath}
otherwise you get the original (more or less undocumented)\cases
command that is defined in latex but really comes from plain tex and should not be used