Orlik earned in 1961 his bachelor"s degree from the Norwegian Institute of Technology in Trondheim and in 1966 his Doctor of Philosophy from the University of Michigan under Frank Raymond with thesis Necessary conditions for the homeomorphism of Seifert manifolds.
He became in 1966 an assistant professor and in 1973 a full professor at the University of Wisconsin-Madison. Orlik was in the academic year 1971/72 a visiting professor in Oslo. From 1967 to 1969 he was a visiting scholar at the Institute for Advanced Study.
Orlik is the author of over 70 publications.
He works on Seifert manifolds, singularity theory, braid theory, reflection groups, invariant theory, and hypergeometric integrals. He was, with Hiroaki Terao and Louis Solomon, a pioneer of the theory of arrangements of hyperplanes.
In 2012 he was elected a Fellow of the American Mathematical Society.
