After graduation, Dunning commenced a doctoral program at Columbia University. In 1932, James Chadwick discovered the neutron, which influenced Dunning's career, as he thereafter devoted much of his professional interest to the characteristics and uses of this particle. Dunning's research was enthusiastically supported at Columbia by George B. Pegram. In 1933, Dunning was an instructor at Columbia University from 1929 to 1932, and a university fellow from 1932 to 1933. He received his Ph.D. in 1934, writing his thesis on "The Emission and Scattering of Neutrons" under Pegram's supervision.