Camillo De Lellis

PI of Initiative on the Geometry of Flows. Professor at the Institute for Advanced Study (IAS), Princeton.

Research topic 

Broadly speaking my research focuses on geometric analysis and partial differential equations. As a student I started working in the calculus of variations (more specifically in geometric measure theory) under the supervision of Luigi Ambrosio. With time my interests have branched towards more classic partial differential equations (systems of conservation laws, transport equations, Hamilton-Jacobi equations, the incompressible Euler equations, Navier-Stokes equations) and minimal surfaces in Riemannian manifolds. In all these fields I am typically interested in the formation and behavior of singularities (or, in some lucky cases, in the absence of singularities).

Biography 

Camillo De Lellis was born in 1976 in San Benedetto del Tronto, Italy. After earning his undergraduate degree in mathematics at the University of Pisa in 1999, he wrote his doctoral dissertation in 2002 under the supervision of Luigi Ambrosio at the Scuola Normale Superiore di Pisa. He joined the faculty of the University of Zurich in 2004 as Assistant Professor of Mathematics, and he was appointed Full Professor in 2005. In 2018 he moved to the Institute for Advanced Study in Princeton, where he holds the IBM von Neumann Professorship. He is active in the fields of calculus of variations, geometric measure theory, hyperbolic systems of conservation laws and fluid dynamics.

Publication and Awards

Publications

• Tristan Buckmaster, Camillo De Lellis, Philip Isett, and L´aszl´o Sz´ekelyhidi, Jr. Anomalous dissipation for 1/5-H¨older Euler flows. Ann. of Math. (2), 182(1):127–172, 2015.
• Gianluca Crippa and Camillo De Lellis. Estimates and regularity results for the DiPerna-Lions flow. J. Reine Angew. Math., 616:15–46, 2008.
• C. De Lellis, F. Ghiraldin, and F. Maggi. A direct approach to Plateau’s problem. J. Eur. Math. Soc. (JEMS), 19(8):2219–2240, 2017.
• Camillo De Lellis. Blowup of the BV norm in the multidimensional Keyfitz and Kranzer system. Duke Math. J., 127(2):313–339, 2005.
• Camillo De Lellis, Guido De Philippis, Jonas Hirsch, and Annalisa Massaccesi. On the boundary behavior of mass-minimizing integral currents. Mem. Amer. Math. Soc., 291(1446):v+166, 2023.
• Camillo De Lellis and Stefan M¨uller. Optimal rigidity estimates for nearly umbilical surfaces. J. Differential Geom., 69(1):75–110, 2005.
• Camillo De Lellis, Stefano Nardulli, and Simone Steinbr¨uchel. An Allard-type boundary regularity theorem for 2d minimizing currents at smooth curves with arbitrary multiplicity. Publ. Math. Inst. Hautes´Etudes Sci., 140:37–154, 2024.
• Camillo De Lellis, Felix Otto, and Michael Westdickenberg. Structure of entropy solutions for multi-dimensional scalar conservation laws. Arch. Ration. Mech. Anal., 170(2):137–184, 2003.
• Camillo De Lellis and Emanuele Spadaro. Regularity of area minimizing currents II: center manifold. Ann. of Math. (2), 183(2):499–575, 2016.
• Camillo De Lellis and Emanuele Spadaro. Regularity of area minimizing currents III: blow-up. Ann. of Math. (2), 183(2):577–617, 2016.
• Camillo De Lellis and Emanuele Nunzio Spadaro. Q-valued functions revisited. Mem. Amer. Math. Soc., 211(991):vi+79, 2011.
• Camillo De Lellis and L´aszl´o Sz´ekelyhidi, Jr. The Euler equations as a differential inclusion. Ann. of Math. (2), 170(3):1417–1436, 2009.
• Camillo De Lellis and L´aszl´o Sz´ekelyhidi, Jr. Dissipative continuous Euler flows. Invent. Math., 193(2):377–407, 2013.

Awards

• Stampacchia Medal (2009)
• Fermat Prize (2013)
• Caccioppoli Prize (2014)
• Bôcher Memorial Prize (2020)
• Maryam Mirzakhani Prize (2022)
• Invited speaker at ICM (2022) and plenary speaker at ECM (2012)
• Member of Academia Europaea, German Leopoldina, and American Academy of Arts \& Sciences
  
  De Lellis has been invited speaker at the International Congress of Mathematicians at Hyderabad in 2010, plenary speaker at the European Congress of Mathematics in Krakow in 2012 and plenary speaker at the Interntional Congress of Mathematicians in 2022. He is a member of the Academia Aeuropea, of the German Academy of Sciences, of the American Academy of Arts and Sciences, and of the Accademia dei Lincei. He is the recepient of the 2009 Stampacchia Medal, 2013 SIAG/APDE Prize (jointly with La'szlo' Sze'kelyhidi Jr.), 2013 Fermat Prize (jointly with Martin Hairer), 2014 Caccioppoli prize, 2015 Amerio Prize, 2020 Bocher Prize (jointly with Larry Guth and Laure Saint-Raymond), 2020 Feltrinelli prize, and 2021 Myriam Mirzakhani prize.