# Manuel Kauers: *Separating Variables in Polynomial Ideals*

For a given ideal $I\subseteq K[x_1,\dots,x_n,y_1,\dots,y_m]$ in a polynomial ring with $n+m$ variables, we want to find all elements that can be written as $f-g$ for some $f\in K[x_1,\dots,x_n]$ and some $g\in K[y_1,\dots,y_m]$, i.e., all elements of $I$ that contain no term involving at the same time one of the $x_1,\dots,x_n$ and one of the $y_1,\dots,y_m$. We cannot solve this problem in full generality, but we report on some constructive results in this context that were first obtained in collaboration with Buchacher and Pogudin and recently generalized further in collaboration with Buchacher.