• About SNS

    The Scuola Normale Superiore is a public institute for higher education that in its two centuries of life has earned itself a special place, both in Italy and abroad, a place characterised by merit, talent and scientific rigour.  Two types of course are available: the undergraduate course and the PhD course.The teaching activity is distributed among three academic structures: the Faculty of Humanities, the Faculty of Mathematical and Natural Sciences, placed in Pisa, and the Institute of Humanities and Social Sciences, located in Palazzo Strozzi in Florence. 

  • Admission

    The evaluation for entrance to the first year of the undergraduate course does not include the high school leaving certificate, and the bachelor's degree is not taken into consideration in the entrance examination for the fourth year course. For each PhD course, candidates’ level of competence, talent, motivations and aptitudes to scientific research will be assessed on the basis of their qualifications and research project and an interview.

  • Academics

    The Scuola Normale Superiore offers two types of course: the undergraduate course, leading to first and second level university degrees, and the PhD course, the international equivalent of the Italian Dottorato di ricerca.The teaching and research activity is distributed among three academic structures: the Faculty of Humanities, the Faculty of Mathematical and Natural Sciences, and the Institute of Humanities and Social Sciences.The first two academic structures, housed at the Pisa site, organize courses for both the  undergraduate course and the PhD course. The Institute of Humanities and Social Sciences, situated in Palazzo Strozzi in Florence, deals only with the PhD course.

  • Research

    A highly qualifying feature of the Normale way is the strong link between teaching and research that is a characteristic of both the undergraduate and the graduate programmes of the Scuola. The research structures of the two Faculties welcome students with a relevant study interest, enabling them to collaborate in a mature way with the activities of the researchers.

  • International

    The Scuola Normale is an institute of a decidedly international nature. Examinations for admission to the undergraduate degree course and for the PhD course are open to all citizens worldwide. A certain number of places on the PhD course are reserved for students from other countries. During the pre laurea and  post lauream teaching courses, study and research programmes are made available at overseas universities and research centres with which the Scuola forms an intense network of collaboration.  The doctorate course in particular is taught in a veritable graduate school in line with the highest international standards. 

AMBROSIO Luigi
Prof. Luigi AMBROSIO
Full Professor
MATHEMATICAL ANALYSIS
Tel. +39 050 509255
WORKPLACE

Palazzo della Carovana

Classe di Scienze Matematiche e Naturali
Piazza dei Cavalieri, 7
56126, PISA

Born in 1963 in Alba, Italy

EDUCATION

1985-1988 Scuola Normale Superiore
Corso di Perfezionamento (PHD).

1981-1985 Scuola Normale Superiore
Pisa, Italy.

1981-1985 Laurea in Matematica (B.S.)
University of Pisa, Italy. Summa cum laude.
Advisor: Prof. Ennio De Giorgi. Thesis in semicontinuity and relaxation of
integral functionals defined on Sobolev spaces.

PROFESSIONAL EXPERIENCE

1997–present Full Professor
Scuola Normale Superiore, Pisa, Italy.

1995–1997 Full Professor
Department of Mathematics, University of Pavia, Italy.

1994–1995 Full Professor
University of Benevento, Italy.

1992–1994 Associate Professor
University of Pisa, Italy.

1988-1992 Research Assistant
Second University of Rome, Italy

HONORS
Long term visiting scientist in the Max Planck Institute of Leipzig, the Massachussets
Institut of Technology, the ETH of Zurich, the Institute Henri Poincare
1991 Bortolozzi" Prize of Unione Matematica Italiana.
1996 National Prize for Mathematics and Mechanics of the italian Minister of Education.
1996 Invited speaker at the 2nd European congress of mathematicians in Budapest.
1999 Caccioppoli" Prize of the Unione Matematica Italiana.
1999 Editor of \Interfaces and Free Boundaries", Main Editor of the \Journal of the European Mathematical Society" until 2011
2000 Editor of \Archive for Rational Mechanics and Analysis" until 2011.
2002 Invited speaker at the International Congress of Mathematicians in Beijing, in the PDE session
2003 Awarded with the international Fermat Prize of the University of Toulouse (France)
2003 Member of the scientic committee of the fourth European Congress of Mathematics
2005 Managing Editor of \Calculus of Variations and Partial Dierential Equations"
2005 Editor of Communications in Partial Dierential Equations
2005 Socio Corrispondente Accademia Nazionale dei Lincei, Roma
2006 Socio Corrispondente Istituto Lombardo, Accademia di Scienze e Lettere, Milano Editor of Mathematical Models and Methods in Applied Sciences
2007 His paper on ows associated to BV vector elds described in the seminaire Bourbaki, expose 972
2008 Plenary speaker at the fth European Congress of Mathematics in Amsterdam
2009 Member of the selection committee for the ICM 2010, PDE session
2011 Editor of Geometric and Functional Analysis.
2013 His papers on gradient ows described in the seminaire Bourbaki, expose 1065

TEACHING ACTIVITY
Has been teaching courses on Γ-convergence, Measure Theory, Elementary Probability, Non Linear
PDE’s, BV functions, Minimal Surfaces and Geometric Measure Theory, Functional Analysis,
Viscosity solutions, Calculus of Variations, Optimal Mass Transportation

RESEARCH TRAINING
Master theses: Carlo Mantegazza, Riccardo Scopigno, Matteo Novaga, Mario Romeo, Camillo
De Lellis, Aldo Pratelli, Vito Iacovino, Nicola Gigli, Davide Vittone, Gianluca Crippa, Alessio
Figalli, Francesco Ghiraldin, Costante Bellettini, Pietro Siorpaes, Eris Runa, Matteo Scienza,
Francesco Ghiraldin, Mirchea Petrache, Alessandro Carlotto, Eris Runa, Gennady Uraltsev, Si-
mone Di Marino, Federico Stra, Roberto Da Luiso,
PhD theses (advisor):
1999. Francois Ebobisse
2002. Matteo Focardi, Camillo De Lellis, Valentino Magnani
2003. Aldo Pratelli
2006. Stefania Maniglia, Davide Vittone
2007. Alessio Figalli
2008. Gianluca Crippa, Nicola Gigli
2009. Edoardo Mainini.
2012. Francesco Ghiraldin, Guido De Philippis

Publications