J. (Jean) François Treves (born April 23, 1930, in

Brussels Brussels (french: Bruxelles or ; nl, Brussel ), officially the Brussels-Capital Region (All text and all but one graphic show the English name as Brussels-Capital Region.) (french: link=no, Région de Bruxelles-Capitale; nl, link=no, Bruss ...

) is an American mathematician, specializing in

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s. Trèves earned his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is a ...

in 1958 from Paris-Sorbonne University under the supervision of

Laurent Schwartz Laurent-Moïse Schwartz (; 5 March 1915 – 4 July 2002) was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields Medal in 19 ...

. He then went to the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...

where from 1958 to 1960 he was assistant professor at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

. From 1961 to 1964 he was an associate professor at Yeshiva University, and from 1964 to 1970 professor at

Purdue University Purdue University is a public land-grant research university in West Lafayette, Indiana, and the flagship campus of the Purdue University system. The university was founded in 1869 after Lafayette businessman John Purdue donated land and money ...

. In 1970 he became a professor at

Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's ...

, and then, in 1984, Robert-Adrian professor of mathematics. He became professor emeritus in 2005. In 1972 he received the

Chauvenet Prize The Chauvenet Prize is the highest award for mathematical expository writing. It consists of a prize of $1,000 and a certificate, and is awarded yearly by the Mathematical Association of America in recognition of an outstanding expository article ...

fo
"On local solvability of linear partial differential equations"
in the Bulletin of the AMS (Volume 76, 1970, pp. 552–571). It was about the problem he worked in 1962 with Louis Nirenberg with whom he found necessary and sufficient conditions for the solvability of equations with analytic coefficients, 1969 (Comptes Rendus de l'Académie des Sciences Paris Bd.269). The question was first presented to him in 1955 by Schwartz as a thesis problem. In 1977 he was

Guggenheim Fellow Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

. In 1991 he received the

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

for his book on

pseudo-differential operator In mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the theory of partial differential equations and quantum field theory, e.g. in ...

s and Fourier integral operators. In 2003 he became a foreign member of the Brazilian Academy of Sciences. In 1970 he was an

invited speaker at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

in Nice (''Hamiltonian fields, bicharacteristic strips in relation with existence and regularity of solutions of linear partial differential equations''). He is a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Writings

Articles

*"On the theory of linear partial differential operators with analytic coefficients." Transactions of the American Mathematical Society 137 (1969): 1–20. *"An abstract nonlinear Cauchy-Kovalevska theorem." Transactions of the American Mathematical Society 150, no. 1 (1970): 77–92. *"Differential polynomials and decay at infinity." Bulletin of the American Mathematical Society 66, no. 3 (1960): 184–186. *"Discrete phenomena in uniqueness in the Cauchy problem." Proceedings of the American Mathematical Society 46, no. 2 (1974): 229–233. *with Howard Jacobowitz: "Nowhere solvable homogeneous partial differential equations." Bulletin of the American Mathematical Society 8, no. 3 (1983): 467–469. *with Nicholas Hanges: "On the analyticity of solutions of first-order nonlinear PDE." Transactions of the American Mathematical Society 331, no. 2 (1992): 627–638.

Books

* * * * * * * * *

References

External links

* Trèves
''On local solvability of linear partial differential equations.''
BAMS 1970

* {{DEFAULTSORT:Treves, Francois Fellows of the American Mathematical Society 1930 births Living people Operator theorists PDE theorists 20th-century French mathematicians 21st-century French mathematicians Purdue University faculty Rutgers University faculty Yeshiva University faculty Paris-Sorbonne University alumni University of California, Berkeley faculty Scientists from Brussels