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Mathematical Physics

Photograph of Yvonne Choquet-Bruhat

Yvonne Choquet-Bruhat

Additional Information

Important Contributions:

She applied fundamental mathematical results to provide a firm basis for the solutions of the classical field equations of physics, most importantly those of general relativity and other theories of gravitation, supergravity, and the non-Abelian gauge theories of the standard model.

Some Important Publications:

"Theoreme d'Existence pour Certains Systemes d'Equations aux Derivees Partielles non Lineaires," Acta Mathematica, 88: 141 (1952)

  • This is the author's (French) thesis, a magisterial work. It exhaustively discusses the Cauchy problem for a system of second order partial differential equations, linear in second derivatives, having special relevance to the Einstein equations in general relativity. The list of results is lengthy and includes deep result on exterior solutions and their uniqueness, on propagation velocity of gravitational excitations, etc.

"Theoremes d'Existence en Mecanique des Fluides Relativistes," Bulletin de la Soc. Math. de France, 86: 155 (1958)

  • The first careful study of existence theorems for non-analytic solutions of the Einstein equations with various types of matter including Kaluza-Klein unified, 5-dimensional, extensions. It established that these general cases define hyperbolic systems with well-defined Cauchy problem.

"Ondes Asymptotiques et Approchees pour des Systemes d'Equations aux Derivees Partielles non Lineaires," J. Maths. Pures et App. 48: 117 (1969)

  • A general method is presented that enable one to construct asymptotic and approximate wave solutions about a given solution for nonlinear system of equations; this extends important earlier work, and also shows when the Cauchy problem becomes ill-posed. Applications are made to gravity.

"Global Solutions of the Problem of Constraints on a Closed Manifold," Symposia Matematica, (in the series Pubblicazione dell'Istituto Nazionale di Alta Matematica) 12: 317 (1973)

  • The problem of existence and uniqueness of global solutions of the constraint equations of general relativity is studied in the important case of a closed manifold, using general elliptic equation methods. The essential results are that existence depends on delicate properties of the manifold and on the sources of the metric; the various cases are carefully classified.

"Existence of Global Solutions of the Yang-Mills, Higgs, and Spinor Field Equations in 3+1 Dimensions," (with D. Christodoulou) Ann. E.N.S. 4th Series 14: 481 (1981)

"Causalite des Theories de Supergravite," Societe Mathematique de France, Asterisque 79-93 (1984)

  • This is perhaps the first study by a mathematician of supergravity, the generalization of Einstein theory unified, by a Grassmannian gauge invariance, with a massles spin 3/2 fermionic field. In particular, the author extends to supergravity the classic causality theorems that hold in the purely geometric bosonic theory. The results are extended both to N>1 supergravitie and to higher dimensions, in particular to the currently important maximal D=11 model.

An important text and reference book:

Analysis, Manifolds and Physics   (co-authored with C. DeWitt-Morette and M. Dillard-Bleick), North Holland Publishing Co., Amsterdam 1977 (revised edition 1982) ; 2 volumes.


Médaille d'Argent du Centre National de la Recherche Scientifique, 1958
Prix Henri de Parville of the Academie des Sciences, 1963
Member, Académie des Sciences, Paris (elected 1979)
Elected to the American Academy of Arts and Sciences 1985
Commandeur de la Légion d'honneur, 1997


1949-51 Research Assistant/Associate, Centre National de la Recherche Scientifique
1951-52 Member, Institute for Advance Study, Princeton
1953-58 Professor, Faculte des Sciences de Marseille
1958-59 Professor, Universite de Reims
1960-    Professeur Titulaire, Faculte des Sciences de Paris and l'Universite Pierre et Marie Curie


Agrégée de mathématiques, Ecole normale supérieure de Sèvres 1946
Docteur ès sciences, Ecole normale supérieure de Sèvres 1951

Sources and References consulted:

Professor Yvonne Choquet-Bruhat, Professor Stanley Deser, [wwf1995], Association for Women in Mathematics Website

Additional Information/Comments:

She has more than 190 published papers on mathematics and mathematical physics.

Her father, Georges Bruhat, was professor of physics at the Sorbonne.

Married to Gustave Choquet with whom she has two children, Geneviève and Daniel; and a third from a previous marriage, Michelle Fourès.

Her recreations include walking and cycling.

Field Editor: Professor Stanley Deser


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latest revision {4/30/97 mjw} 3/16/01 nb