Rainer earned his PhD in 2014 from the University of Konstanz, Germany, advised by Claus Scheiderer. He then spent three months in Daejeon, South Korea, attending the Thematic Program on Applied Algebraic Geometry at the National Institute of Mathematical Sciences, before moving to a postdoc position at the Georgia Institute of Technology.
During the summer of 2017, he joined the working group of Bernd Sturmfels studying nonlinear algebra at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany. Rainer also attended the MSRI program on Geometric and Topological Combinatorics. Since October 2017, he has been a Juniorprofessur (roughly equivalent to an assistant professor) at the Free University Berlin, in Günter Ziegler's Discrete Geometry working group.