Dirks was the first graduate student in the laboratory of Niles Pierce at Caltech.  His dissertation was entitled "Analysis, design, and construction of nucleic acid devices".
Dirks' work in computational chemistry involved creating algorithms and computational tools for the analysis of nucleic acid thermodynamics and nucleic acid structure prediction. Dirks wrote the initial code for the NUPACK suite of nucleic acid design and analysis tools, which generates base pairing probabilities through calculation of the statistical partition function. Unlike other structure prediction tools, NUPACK is capable of handling an arbitrary number of interacting strands rather than being limited to one or two. Dirks also developed an algorithm capable of efficiently handling certain types of pseudoknots, a class of structure that is more computationally intensive to analyze, although NUPACK only implements this ability for single RNA strands.
His experimental work pioneered the hybridization chain reaction method, the first demonstration of the self-assembly of nucleic acid structures conditional on a molecular input. The method arose from attempts to use DNA hairpins as "fuel" for DNA machines, but Dirks and Pierce realized that they could instead be used for signal amplification, and when used in conjunction with an aptamer, as a biosensor. As an enzyme-free, isothermal method, it later found application as the basis of an immunoassay method, for in situ hybridization imaging of gene expression, and as the basis for catalytic, isothermal self-assembly of DNA nanostructures.
Dirks then worked at D. E. Shaw Research in Manhattan to develop methods for computational protein structure prediction for the design of new drugs, beginning in 2006.