Faculty Directory

Contact Information

Stratton Hall, Room 108

View Personal Website

Luca Capogna

My research is in the area of Partial Differential Equations. I am also interested in Calculus of Variations and in analytic aspects of Quasiconformal Mappings, Sub-Riemannian Geometry, Minimal Surfaces and Mean Curvature Flow.

Partial differential equations, and more in general Mathematics, provide a powerful language to express our understanding of complex phenomena in nature and in other contexts. The equilibrium and tension between pure mathematics and the applications that have motivated it is a source of never ending discovery and fascination for me.

I enjoy teaching and communicating mathematics. It is very important to be able to convey the relevance of mathematicians’ research to students, to scientists in other disciplines and to the community at large. At the same time it is also crucial to be able to receive ideas and open problems from these communities and invest in mathematical research that is relevant to them.

WPI, with its mix of practice and theory, is an ideal place to continue my work, both as a researcher and as an educator.

Research Interests

  • Partial Differential Equations


  • BS, Second University of Rome, Italy
  • PhD, Purdue University 1996
  • Postdoc at Courant Institute of Mathematical Sciences (1996-1998), University of Pennsylvania (1998-1999)

Featured Publications

  •  "An introduction to the Heisenberg Group and to the sub-Riemannian Isoperimetric problem", with D. Danielli, S. Pauls and J. Tyson. Birkhäuser , "Progress in Mathematics". 2007, Approx. 230 p.
  • Sub-Riemannian Heat Kernels and Mean Curvature of graphs,  Jour. of Functional Analysis, Volume 264, Issue 8, 15 April 2013, Pages 1899–1928 (with Giovanna Citti and Cosimo Senni Guidotti Magnani). (2013)
  • "$1-$Quasiconformal maps in Carnot groups" Duke Math. Journal Vol. 135, No. 3 (2006) (with Michael Cowling).
  • Legendrian energy minimizers.,
(with Fang-Hua Lin) Calc. Var. Partial Differential Equations 12 (2001), no. 2, 145--171.
  • Regularity for quasilinear equations in the Heisenberg group,
Communications in Pure and Applied Mathematics vol. L, (1997), pages 867--889.

Full list of publications

Professional Highlights

  • 2002 NSF Early Career Award
  • Alfred P. Sloan doctoral dissertation fellowship: 1995-1996
  • Institute for Mathematics and its Applications, Associate Director, 2011-2013
  • Email a Friend
  • Bookmark this Page
  • Share this Page