Luca Capogna

Luca Capogna is the Mary Augusta Jordan Professor of Mathematical Sciences at Smith College. Prior to joining Smith, he held positions as a Courant Instructor at NYU, a Rademacher Instructor at the University of Pennsylvania, and tenured positions at the University of Arkansas and Worcester Polytechnic Institute (where he served as department head from 2013-2020). From 2011-2013, he was a visitor at the University of Minnesota, serving as associate director of the Institute for Mathematics and its Applications (IMA).

Capogna earned his Ph.D. from Purdue University and his B.S. from the Second University of Rome, Tor Vergata (Italy).

His research spans analysis and partial differential equations, with specific interests in quasiconformal mappings, sub-Riemannian geometry, and geometric flows. In recent years, he has expanded his research to include machine learning applications, particularly using neural networks for system identification problems. His work demonstrates a strong connection between classical mathematical analysis and modern computational techniques.

Capogna's publication record shows a clear evolution from pure mathematical analysis (particularly in sub-Riemannian geometry and PDE theory) to more applied work incorporating machine learning. His recent publications (2021-2024) increasingly focus on neural networks, system identification, and deep learning applications, while maintaining strong connections to his foundational work in analysis.

• Mary Augusta Jordan Professorship at Smith College

Capogna has collaborated extensively with researchers including Giovanna Citti, Mario Bonk, and Enrico Le Donne. His work has been supported by various research grants, including an NSF RUI grant titled 'PDE and Geometry in non-smooth spaces' (2024). He has served in leadership roles, including as department head at Worcester Polytechnic Institute and associate director of the IMA at the University of Minnesota.

His research has significant implications for both theoretical mathematics and practical applications in system modeling and identification, bridging the gap between pure mathematical analysis and modern computational approaches.