Juris Hartmanis: fundamental contributions to isomorphism problems

The author surveys Hartmanis´ contributions to isomorphism problems. These problems are primarily of two forms: first, isomorphism problems for restricted programming systems, including the Hartmanis-Baker conjecture that all polynomial time programming systems are polynomially isomorphic; and second, the research on isomorphisms, and particularly polynomial time isomorphisms, for complete problems for various natural complexity classes, including the Berman-Hartmanis conjecture that all sets complete for NP under Karp reductions are polynomially isomorphic. In addition to the work of Hartmanis and his students, the author discusses some of the impact that this research has had on other topics and other researchers in structural complexity theory