Alberto Tognoli (born 26 July 1937,

Brescia Brescia (, locally ; lmo, link=no, label= Lombard, Brèsa ; lat, Brixia; vec, Bressa) is a city and ''comune'' in the region of Lombardy, Northern Italy. It is situated at the foot of the Alps, a few kilometers from the lakes Garda and Iseo. ...

, died 3 March 2008 in

Rapallo Rapallo ( , , ) is a municipality in the Metropolitan City of Genoa, located in the Liguria region of northern Italy. As of 2017 it had 29,778 inhabitants. It lies on the Ligurian Sea coast, on the Tigullio Gulf, between Portofino and Chiavar ...

) was an Italian mathematician, who worked on algebraic geometry. Tognoli received his Ph.D. (Laurea) in 1960 from the University of Pisa. From 1970 he became full professor at the same university, and he also taught in Cosenza, Ferrara, Paris and Tours. He was also a professor of geometry at the

University of Trento The University of Trento (Italian: ''Università degli Studi di Trento'') is an Italian university located in Trento and nearby Rovereto. It has been able to achieve considerable results in didactics, research, and international relations accor ...

from 1986 until his retirement as professor emeritus in 2005. He is known for his research on Nash functions and Nash manifolds (named after John Nash). He proved Nash's conjecture that smooth compact manifolds are diffeomorphic to non-singular real algebraic manifolds (known as the Theorem of Nash and Tognoli). He received in 1974 the

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 Cacci ...

and in 1988 the Gold Medal in Mathematics of the Accademia dei XL. Selected publications *Algebraic Geometry and Nash Functions, Institutiones Mathematicae, Academic Press 1978 *as editor with M. Galbiati: Real analytic and algebraic geometry : proceedings of the conference held in Trento, Italy, October 3–7, 1988, Lecture Notes in Mathematics 1420, Springer Verlag 1990 *Singularities of Analytic Spaces, CIME, Rom: Cremonese 1975 *Introduzione alla teoria degli spazi analitici reali, Rom, Accademia dei Lincei 1976 *Approximation theorems and Nash conjecture, Memoires SMF, 38, 1974, 53-68
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*Algebraic approximation of manifolds and spaces, Seminaire Bourbaki, No. 548, 1979/80
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* *with Alessandro Tancredi:

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zione Scientifica – Alberto Tognoli
{{DEFAULTSORT:Tognoli, Alberto 1937 births 2008 deaths Italian mathematicians University of Pisa alumni Academic staff of the University of Trento