[2] He has worked in the fields of operator theory, Hilbert space operators, control theory, algebraic geometry, and noncommutative computer algebra during his career.
[3] He organized the first International Workshop on Operator Theory and its Applications which has spawned revolutionary cross-discipline research for over forty years.
The theoretical studies of amplifier design by Helton and Youla were the first papers in the now ubiquitous area called H-infinity engineering.
His seminal result in this area is the non-commutative version of Hilbert's Nullstellensatz.
[6] A related interest is computer algebra and Helton’s research group has been the main provider to Wolfram Mathematica of general non-commutative computer algebra capability.