Martin Lorenz's research interests encompass several areas of noncommutative algebra. He has worked on topics in ring theory, group theory, Hopf algebras, algebraic K-theory and other fields. For about ten years, Lorenz's research was focused on multiplicative invariant theory. His monograph with that title was published by Springer-Verlag in 2005. Subsequently, Lorenz has worked on applications of Koszul algebras to algebraic combinatoris and, most recently, on algebraic group actions on noncommutative spaces.