Translation:The university of technology conducts research on computers.
Neither: They conduct research after computers. The whole sentence suffers from the slight differences between the expressions of the two languages. As it happens, "onderzoek doen naar" ("onderzoek", by the ways is less abstract than "research"; e.g. one could do "een onderzoek") is mostly research about the existence or non-existence. Thus, we're talking here about someone specifically doing tests to determine whether computers exist.
The "conducts research" is fine in general, but it should probably be "is researching" to make it less abstract.
"In the field of" would best translate to "op het gebied van" I would say. Having a look on Google I also see a fair amount of "in het gebied van", I had a look if I could find a reference somewhere on if that would be correct but have not been able to find that (yet).
Anyway "op het gebied van" is always correct, "in het gebied van" might be right, but might also be the result of people using "in the field of" and changing the "op" for "in" as a result.