UMI CACCIOPPOLI PRIZE
UMI - Italian Mathematical Union

Winners

1960 Ennio De Giorgi
1962 Edoardo Vesentini
1964 Emilio Gagliardo
1966 Enrico Bombieri
1968 Mario Miranda
1970 Claudio Baiocchi
1974 Alberto Tognoli
1978 Enrico Giusti
1982 Antonio Ambrosetti
1986 Corrado De Concini
1990 Gianni Dal Maso
1994 Nicola Fusco
1998 Luigi Ambrosio
2002 Giovanni Alberti
2006 Andrea Malchiodi
2010 Giuseppe Mingione

Caccioppoli Prize 1960 - Ennio De Giorgi (Scuola Normale Superiore di Pisa)

Ennio De Giorgi

Committee's citation

Ennio De Giorgi's high level scientific activity led him to gain full professorship in 1958. Amongst his contributions, we mention, in chronological order The results obtained by Professor De Giorgi demonstrate his great talent and put him in the front line of young Italian analysts.

Ennio De Giorgi on MacTutor History of Mathematics archive


Caccioppoli Prize 1962 - Edoardo Vesentini (University of Pisa)

Edoardo Vesentini photo courtesy of MFO

Committee's citation

Edoardo Vesentini's high level scientific activity is mainly devoted to Topology and to Complex Analysis, and in particular to the study of complex algebraic varieties.

After his first publications (amongst which we mention one paper dedicated to the study of polarity of algebraic curves and another one where an intrinsic proof of Riemann-Roch theorem is obtained), there must be recalled his proof of a fundamental theorem connecting, via duality, the homology classes of canonical varieties of an algebraic variety with the Chern's cohomology classes, and his deep papers on jacobians of several meromorphic functions on a complex variety, that generalize the classical results related to algebraic varieties.

In the last years Vesentini started a fruitful cooperation with other brilliant mathematicians that eventually led to very interesting results on non-compact complex varieties related to Kodaira's embedding theorem.

The brilliant and deep work of Vesentini, demonstrating a masterly use of modern topological, geometrical and analytical methods, and the importance of the results he achieved, clearly qualify him as one of the best young Italian mathematicians.

Edoardo Vesentini on Wikipedia (Italian)


Caccioppoli Prize 1964 - Emilio Gagliardo (University of Genova)

Emilio Gagliardo

Committee's citation

Gagliardo's scientific production stands at very high levels, and gained very high international recognition.

After some early, interesting contributions, amongst which we single out those on second order parabolic equations, he obtained, under the guidance of Caccioppoli, a compactness criterion with respect to mean convergence. In turn, this led him to give a characterization of boundary traces that was the starting point for the work of several authors, especially from Russia.

Further remarkable results of Gagliardo are those on Sobolev spaces, including some generalizations of a few inequalities due to Sobolev himslef. Gagliardo obtained important results in Interpolation Theory. In particular, he was the first to build an interpolation theory for Banach spaces. Further, more recent results of Gagliardo are concerned with integral transformations between Lebesgue spaces. The results of Gagliardo show that he is a very original analyst, and obviously put him amongst the best young Italian mathematicians.

Emilio Gagliardo on Wikipedia (Italian)


Caccioppoli Prize 1966 - Enrico Bombieri (University of Pisa)

Enrico Bombieri

Committee's citation

Enrico Bombieri's scientific production is mainly concerned with Number theory, Algebraic geometry and Analytic number theory, and includes results of the highest level. It demonstrates Bombieri's abilities to deal with very modern tools of different kinds used to solve very difficult and fundamental problems. His results have obtained clear international recognition. Beside a few papers mainly dealing with the Geometry of numbers, we mention: a group of papers devoted to Selberg's formulas for the estimation of rests in the "Prinzahlsatz" and their generalization to a class of arithmetic functions, according to S.A Amitsur's viewpoints; yet, we mention a paper about Tu. V. Linnik's "large sieve". This last one, in which a very ingenious Abel-type inequality on double sums is employed, eventually leads to a theorem that in many applications can be used to replace the extended Riemann hypothesis (see for instance a paper on small differences of consecutive prime numbers). In the field of Analytic functions, beside a few papers on meromorphic functions, he mainly worked on the Bierberbach conjecture on univalent functions.

As for his work in Algebraic geometry, we mention two particularly remarkable papers: a first one dealing with the exponential sums related to the L-function introduced by Artin and Schreirer, and another one (written with Swinnerton-Dyer) on the Artin's Z-function of the cubic hypersurface in the four dimensional projective space. For this case it is possible to verify the validity of the Riemann-Weil's conjecture.

Enrico Bombieri on MacTutor History of Mathematics archive


Caccioppoli Prize 1968 - Mario Miranda (University of Pisa)

Mario Miranda photo courtesy of MFO

Committee's citation

Mario Miranda's work, building on previous DeGiorgi's one, led to fundamental contributions to the theory of minimal surfaces.


Caccioppoli Prize 1970 - Claudio Baiocchi (University of Pavia)

Claudio Baiocchi

Committee's citation

Baiocchi is a high level mathematician who obtained, in a short time, important and original results in various fields of Analysis, and, in particular, on abstract differential equations and their applications to evolutionary problems and in the Interpolation Theory between Banach spaces. He also gave contributions to the problem of determining when the "strong" and "weak" extensions of a differential operator coincide.


Caccioppoli Prize 1974 - Alberto Tognoli (University of Pisa)

Alberto Tognoli photo courtesy of MFO

Committee's citation

In his wide scientific production Tognoli has systematically developed, and has actually contributed to found, a modern theory of real analytic spaces. This theory shows remarkable differences with that of complex analytic spaces due to the appearance of completely new phenomena and problems that Tognoli eventually overcame with his new methods. Amongst his papers the one called "Su una congettura di Nash" stands out. In this paper Tognoli shows how to give an answer to a fundamental approximation problem by mean of cobordism theory methods.


Caccioppoli Prize 1978 - Enrico Giusti (University of Pisa)

Enrico Giusti

Committee's citation

After a few early papers on Schrödinger and wave equations, Giusti devoted himself to the theory of nonlinear elliptic equations. His research is mainly dealing with regularity problems for solutions to the minimal surfaces equation, variational inequalities for minimal surfaces with thin and discontinuous obstacles, partial regularity of solutions to nonlinear elliptic systems. His result on the Bernstein problem, obtained in collaboration with Bombieri and De Giorgi, is of exceptional importance. His whole scientific production features truly remarkable results and shows that Giusti gave important contributions to the solution of difficult problems in nonlinear analysis.

Enrico Giusti on Wikipedia


Caccioppoli Prize 1982 - Antonio Ambrosetti (International School for Advanced Studies, Trieste)

Antonio Ambrosetti photo courtesy of MFO

Committee's citation

The by now very wide scientific production of Prof. Antonio Ambrosetti is mainly concerned with the following topics: Professor Ambrosetti is a remarkably original researcher; when approaching problems, rather than making use of massive technical tools he prefers finding new and often surprising paths. At the origins of Ambrosetti's heuristic approaches we always find the attitude to catch the most basic geometric and intuitive aspects which are typical of the Functional Analysis "in the style of Caccioppoli".

Antonio Ambrosetti on Wikipedia (Italian)


Caccioppoli Prize 1986 - Corrado De Concini (La Sapienza University of Rome)

Corrado De Concini

Committee's citation

The committee proposes to award Prof. Corrado De Concini with the 1986 Caccioppoli prize for his contributions to the Theory of invariants, to the Theory of algebraic groups, to Enumerative geometry, and, in particular, for the solution (obtained with E. Arbarello) of the classical Schottky's problem.

Such works show that De Concini is a very high level mathematician, who is able to use with great skills algebraic, topological and analytical methods towards the solution of difficult problems.

Corrado De Concini on Wikipedia (Italian)


Caccioppoli Prize 1990 - Gianni Dal Maso (International School for Advanced Studies, Trieste)

Gianni Dal Maso

Committee's citation

Gianni Dal Maso is a very high level mathematician and one of the most noteworthy members of the Italian school of Calculus of Variations. His whole scientific production, which already includes more than sixty papers, stands at very high levels; some of its highlights include

Caccioppoli Prize 1994 - Nicola Fusco (University of Naples)

Nicola Fusco

Committee's citation

Nicola Fusco is a refined mathematician who gave substantial contributions to the Calculus of Variations. In his high level scientific production some of the highlights are Nicola Fusco on Wikipedia

Caccioppoli Prize 1998 - Luigi Ambrosio (Scuola Normale Superiore di Pisa)

Luigi Ambrosio

Committee's citation

Luigi Ambrosio is a remarkable mathematician who gave substantial contributions to the Calculus of Variations and to some aspects of the Theory of partial differential equations. In his very high level scientific production, he obtained particularly relevant results on the following topics: Luigi Ambrosio on Wikipedia

Caccioppoli Prize 2002 - Giovanni Alberti (University of Pisa)

Giovanni Alberti

Committee's citation

Giovanni Alberti is one of the most brilliant analysts of his generation. He very soon revealed his talent with by proving a remarkable Lusin type theorem for gradients, that eventually had important applications to semicontinuity and relaxation problems for integral functionals. He proved a deep structure theorem on the distributional derivative of BV maps, which is nowadays known as Rank-one theorem, thereby solving in the positive a conjecture of De Giorgi. He eventually studied subtle problems in the theory of Gamma convergence and in the theory of multiple-scale problems, and developed a general convergence theory for problems of Ginzburg-Landau type in arbitrary dimension and codimension.

Giovanni Alberti on Wikipedia (Italian)


Caccioppoli Prize 2006 - Andrea Malchiodi (International School for Advanced Studies, Trieste)

Andrea Malchiodi

Committee's citation

The work of Andrea Malchiodi is devoted to important problems of variational nature, such as On such topics, Malchiodi obtained several remarkable and original results, that appeared on some of the most prestigious Mathematics journals, and that gained international recognition. In particular, it is worth mentioning his prestigious papers on Q-curvature and those on the existence of solutions to singular perturbation problems concentrating on positive dimension sets. Such results gained a wide international success, making him one of the most brilliant figures in the nowadays Mathematical community.


Caccioppoli Prize 2010 - Giuseppe Mingione (University of Parma)

Giuseppe Mingione

Committee's citation

The vast scientific production of Giuseppe Mingione, which is entirely focused on regularity problems for vectorial integral functionals and nonlinear systems of partial differential equations of elliptic and parabolic type, is rich of remarkable results, that have been obtained by mean of absolutely innovative techniques, in turn based on an original and sometimes surprising way of using Potential theory ideas in the nonlinear setting.

Some of the highlights are

Above all, there must be mentioned two recent papers featuring pointwise gradient estimates for solutions to quasilinear equations via Riesz and Wolff potentials of the data. Such very general estimates allow to obtain in a unified way several results proved in the last thirty years by very different and peculiar techniques, and to fix some borderline cases which were still remaining an open problem.


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