Luigi Ambrosio is a professor at Scuola Normale Superiore in Pisa, Italy.
His main fields of research are the calculus of variations

Calculus of variations

Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...

 and geometric measure theory

Geometric measure theory

In mathematics, geometric measure theory is the study of the geometric properties of the measures of sets , including such things as arc lengths and areas. It uses measure theory to generalize differential geometry to surfaces with mild singularities called rectifiable sets...

.

Luigi Ambrosio is an Italian mathematician known for his contributions to the calculus of variations and geometric measure theory.

Biography

Ambrosio entered the Scuola Normale Superiore di Pisa in 1981. He obtained his degree under the guidance of Ennio de Giorgi

Ennio de Giorgi

-References:. The first paper about SBV functions and related variational problems.. The first note published by De Giorgi describing his approach to Caccioppoli sets.. The first complete exposition by De Giorgi of the theory of Caccioppoli sets.. An advanced text, oriented to the theory of minimal...

 in 1985 at University of Pisa

University of Pisa

The University of Pisa , located in Pisa, Tuscany, is one of the oldest universities in Italy. It was formally founded on September 3, 1343 by an edict of Pope Clement VI, although there had been lectures on law in Pisa since the 11th century...

, and the Diploma at Scuola Normale. He obtained his PhD in 1988.

He is currently professor at the Scuola Normale, having taught previously at the University of Rome "Tor Vergata", the University of Pisa

University of Pisa

The University of Pisa , located in Pisa, Tuscany, is one of the oldest universities in Italy. It was formally founded on September 3, 1343 by an edict of Pope Clement VI, although there had been lectures on law in Pisa since the 11th century...

, and the University of Pavia

University of Pavia

The University of Pavia is a university located in Pavia, Lombardy, Italy. It was founded in 1361 and is organized in 9 Faculties.-History:...

. Ambrosio also taught and conducted research at the Massachusetts Institute of Technology

Massachusetts Institute of Technology

The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...

, the ETH

Eth

Eth is a letter used in Old English, Icelandic, Faroese , and Elfdalian. It was also used in Scandinavia during the Middle Ages, but was subsequently replaced with dh and later d. The capital eth resembles a D with a line through the vertical stroke...

 in Zurich, and the Max-Planck-Institut für Mathematik in den Naturwissenschaften (MIS) to Leipzig.

He is the Managing Editor of the scientific journal Calculus of Variations and Partial Differential Equations, and member of the editorial boards of scientific journals.

Awards

In 1998 Ambrosio won the Caccioppoli Prize

Caccioppoli Prize

The Caccioppoli Prize is awarded by the Italian Mathematical Union to an Italian mathematician not exceeding the age of 38 who established a wide international reputation . The prize is entitled to the memory of the Italian mathematician Renato Caccioppoli and is awarded on the occasion of the...

. In 2002 he was Plenary Speaker at the International Congress of Mathematicians in Beijing and in 2003 he has been awarded with the Fermat Prize

Fermat Prize

The Fermat prize of mathematical research rewards research works in fields where the contributions of Pierre de Fermat have been decisive:* Statements of variational principles* Foundations of probability and analytic geometry* Number theory....

. From 2005 he is a corresponding member of Accademia Nazionale dei Lincei.

Selected publications

• Ambrosio, L. (1989). A compactness theorem for a new class of functions of bounded variation. Boll. Un. Mat. Ital. B (7) 3, no. 4, 857–881.
• De Giorgi, Ennio; Ambrosio, Luigi (1989). New functionals in the calculus of variations. (Italian) Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 82 (1988), no. 2, 199–210.
• Ambrosio, L. (1990). Existence theory for a new class of variational problems. Arch. Rational Mech. Anal. 111, no. 4, 291–322.
• Ambrosio, Luigi; Fusco, Nicola; Pallara, Diego (2000). Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York.
• Ambrosio, L; Kirchheim, B. "Currents in metric spaces", Acta Math., 185 (2000), 1–80.
• Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe (2005). Gradient flows in metric spaces and in the space of probability measures. Lectures in Mathematics ETH Zurich. Birkhהuser Verlag, Basel.