Prior to joining Smith, Luca Capogna was a Courant Instructor at the Courant Institute/NYU and a Rademacher instructor at the University of Pennsylvania. He has held tenured positions at the University of Arkansas and at Worcester Polytechnic Institute, where he also served as department head from 2013 to 2020. In 2011–13, he was a visitor at the University of Minnesota, where he served as associate director of the Institute for Mathematics and its Applications (IMA).

Capogna’s research is in analysis and partial differential equations. He is also interested in analytic aspects of quasiconformal mappings, sub-Riemannian geometry and geometric flows. More recently, he has pursued projects in machine learning, aimed at using neural networks for system identification problems.