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Frédéric Pham (born 17 November 1938 in
Publications de Frédéric Pham
''Singularities of integrals. Homology, hyperfunctions and microlocal analysis''
Springer Verlag, 2011. *''Singularités des systèmes différentiels de Gauss-Manin'', Birkhäuser, 1979. *''Introduction à l’étude topologique des singularités de Landau'', Mémorial des Sciences Mathématiques, vol. 164, Paris, Gauthier-Villars 1967. *with Nguyen Tien Dai and Nguyen Huu Duc: ''Singularités non dégénérées des systèmes de Gauss-Manin réticulés'', Montreuil, Gauthier-Villars, 1981. *as editor: ''Hyperfunctions and theoretical physics'', Springer Verlag, 1975. (Conference at Nice May 1973) *''Singularités des courbes planes: une introduction à la géometrie analytique complexe'', École polytechnique, 1972. *''Fonctions d’une ou deux variables'' Collections Sciences Sup, Dunod, 2003. *''Les différentielles'', Masson, 1996.
''Formules de Picard-Lefschetz généralisées et ramification des intégrales''
Bulletin Societé Mathématique de France, vol. 93, 1965, pp. 333–367.
Frédéric Pham (born 17 November 1938 in Saigon
Ho Chi Minh City (HCMC) ('','' TP.HCM; ), commonly known as Saigon (; ), is the most populous city in Vietnam with a population of around 14 million in 2025.
The city's geography is defined by rivers and canals, of which the largest is Saigo ...
) is a Vietnamese-French mathematician and mathematical physicist. He is known for the Brieskorn-Pham manifolds (explicit examples of exotic sphere
In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold ''M'' that is homeomorphic but not diffeomorphic to the standard Euclidean ''n''-sphere. That is, ''M'' is a sphere from the point of view of ...
s).
Education and career
Pham studied from 1957 to 1959 at theÉcole polytechnique
(, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris.
The school was founded in 1794 by mat ...
. From 1961 to 1969 he worked at Saclay Nuclear Research Centre
The CEA Paris-Saclay center is one of nine centers belonging to the French Alternative Energies and Atomic Energy Commission (CEA). Following a reorganization in 2017, the center consists of multiple sites, including the CEA Saclay site (formerly a ...
, where he developed his doctoral thesis. In addition, during those years, he attended the seminar conducted by René Thom
René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French mathematician, who received the Fields Medal in 1958.
He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became ...
at the Institut des Hautes Études Scientifiques
The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics (also with a small theoretical biology g ...
(IHES). In 1969 Pham received his Ph.D. with supervisor Raymond Stora from Saclay with thesis ''Singularités des processus de diffusion multiple''. He became in 1970 a professor at the University of Nice Sophia Antipolis and retired there in 2001 as professor emeritus. He was a visiting professor in Hanoi
Hanoi ( ; ; ) is the Capital city, capital and List of cities in Vietnam, second-most populous city of Vietnam. The name "Hanoi" translates to "inside the river" (Hanoi is bordered by the Red River (Asia), Red and Black River (Asia), Black Riv ...
for the academic year 1979–1980. He was a frequent visitor at the Institut Fourier in Grenoble
Grenoble ( ; ; or ; or ) is the Prefectures in France, prefecture and List of communes in France with over 20,000 inhabitants, largest city of the Isère Departments of France, department in the Auvergne-Rhône-Alpes Regions of France, region ...
.
His research deals with analytic singularities of Feynman integrals, Landau singularities in S-matrix theory, singularities of systems of plane algebraic curves, microlocal analysis, function theory of several complex variables, semiclassical approximations in quantum mechanics, and Sato's hyperfunction
In mathematics, hyperfunctions are generalizations of functions, as a 'jump' from one holomorphic function to another at a boundary, and can be thought of informally as distributions of infinite order. Hyperfunctions were introduced by Mikio Sato ...
s. Pham in the 1960s applied Thom's methods of differential topology to Landau singularities and in the 1970s worked with Bernard Teissier on singularities of systems of plane algebraic curves.
In 1970 he was an Invited Speaker at the ICM in Nice with talk (''Fractions lipschitziennes et saturation de Zariski des algèbres analytiques complexes'').
Sources
*André Voros and Bernard Malgrange ''Les travaux de Frédéric Pham'', Parts 1,2, Annales de l’Institut Fourier, vol. 53, 2003, p. 957Publications de Frédéric Pham
Selected publications
''Singularities of integrals. Homology, hyperfunctions and microlocal analysis''
Springer Verlag, 2011. *''Singularités des systèmes différentiels de Gauss-Manin'', Birkhäuser, 1979. *''Introduction à l’étude topologique des singularités de Landau'', Mémorial des Sciences Mathématiques, vol. 164, Paris, Gauthier-Villars 1967. *with Nguyen Tien Dai and Nguyen Huu Duc: ''Singularités non dégénérées des systèmes de Gauss-Manin réticulés'', Montreuil, Gauthier-Villars, 1981. *as editor: ''Hyperfunctions and theoretical physics'', Springer Verlag, 1975. (Conference at Nice May 1973) *''Singularités des courbes planes: une introduction à la géometrie analytique complexe'', École polytechnique, 1972. *''Fonctions d’une ou deux variables'' Collections Sciences Sup, Dunod, 2003. *''Les différentielles'', Masson, 1996.
''Formules de Picard-Lefschetz généralisées et ramification des intégrales''
Bulletin Societé Mathématique de France, vol. 93, 1965, pp. 333–367.
References