After gaining his doctorate at Columbia, Dunning continued teaching and research there, becoming an assistant professor in 1935, and an associate professor there in 1938. Dunning was a central figure at Columbia on neutron research, and went on to publish 24 papers on neutrons between 1934 and 1938. In 1936, Dunning received a Traveling Fellowship, which he used to meet and discuss his neutron physics research with many eminent European nuclear physicists including Niels Bohr, James Chadwick, Fermi, Werner Heisenberg, and Ernest Rutherford.