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

Brussels Brussels, officially the Brussels-Capital Region, (All text and all but one graphic show the English name as Brussels-Capital Region.) is a Communities, regions and language areas of Belgium#Regions, region of Belgium comprising #Municipalit ...

) is an American mathematician, specializing in

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s. Trèves earned his Ph.D. in 1958 from

Paris-Sorbonne University Paris-Sorbonne University (also known as Paris IV; ) was a public university, public research university in Paris, France, active from 1971 to 2017. It was the main inheritor of the Faculty of Humanities of the University of Paris. In 2018, it m ...

under the supervision of

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

. He then went to the

United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...

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 university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

. From 1961 to 1964 he was an associate professor at

Yeshiva University Yeshiva University is a Private university, private Modern Orthodox Judaism, Orthodox Jewish university with four campuses in New York City.

, and from 1964 to 1970 professor at

Purdue University Purdue University is a Public university#United States, public Land-grant university, land-grant research university in West Lafayette, Indiana, United States, and the flagship campus of the Purdue University system. The university was founded ...

. In 1970 he became a professor at

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

, 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 an annual award given by the Mathematical Association of America in recognition of an outstanding expository article on a mathematical topic. It consists of a prize of $1,000 and a certificate. The Chauvenet Prize was the ...

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 Louis Nirenberg (February 28, 1925 – January 26, 2020) was a Canadian-American mathematician, considered one of the most outstanding Mathematical analysis, mathematicians of the 20th century. Nearly all of his work was in the field of par ...

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, endowed by the late Simon and Olga Hirsh Guggenheim. These awards are bestowed upon individuals who have demonstrated d ...

. 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 m ...

s and

Fourier integral operator In mathematical analysis, Fourier integral operators have become an important tool in the theory of partial differential equations. The class of Fourier integral operators contains differential operators as well as classical integral operators as ...

s. In 2003 he became a foreign member of the

Brazilian Academy of Sciences Brazilian commonly refers to: * Brazil, a country * Brazilians, its people * Brazilian Portuguese, its dialect Brazilian may also refer to: * "The Brazilian", a 1986 instrumental music piece by Genesis * Brazilian Café, Baghdad, Iraq (1937) * Bra ...

. In 1970 he was an

invited speaker at the International Congress of Mathematicians An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...

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 Partial differential equation 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