Naber is a geometric analyst working on the regularity, singularity, and topology of geometrically motivated equations. His research includes work on the rectifiability of singularities, nonlinear harmonic maps, minimal hypersurfaces, spaces with lower Ricci bounds and the Yang-Mills equations.
In 2014, Naber was named an Alfred P. Sloan Fellow and gave an invited talk at the International Congress of Mathematicians. He was named a Fellow of the American Mathematical Society in 2017. He was awarded the 2018 New Horizons Prize in Mathematics of the Breakthrough Foundation. In 2023 he was named a Simons Investigator in Mathematics.