Sergei Raimondovich Treil (or Treil') (Сергей Раймондович Треиль) is a Russian mathematician, specializing in analysis. At Leningrad State University (now named Saint Petersburg State University), Sergei R. Treil graduated in mathematics in 1982 with an M.Sc. and in 1985 with a Ph.D. His Ph.D. thesis, dealing with geometric aspects of

Hankel operator In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a rectangular matrix in which each ascending skew-diagonal from left to right is constant. For example, \qquad\begin a & b & c & d & e \\ b & c & d & e & ...

s and

Toeplitz operator In operator theory, a Toeplitz operator is the compression of a multiplication operator on the circle to the Hardy space. Details Let S^1 be the unit circle in the complex plane, with the standard Lebesgue measure, and L^2(S^1) be the Hilbert spa ...

s, was supervised by Nikolai Kapitonovich Nikolski. From 1986 to 1989 Treil was an assistant professor at the

Baikonur Baikonur ( ; ) is a city in Kazakhstan on the northern bank of the Syr Darya river. It is currently leased and administered by the Russian Federation as an enclave until 2050. It was constructed to serve the Baikonur Cosmodrome with adminis ...

branch of the

Moscow Aviation Institute Moscow Aviation Institute () is an engineering research university in Moscow, Russia. It is designated a National Research University. Since its inception the institute has been spearheading advances in aerospace technology both within Russia a ...

(MAI). From 1989 to 1991 he was a researcher at the laboratory of theoretical cybernetics at Leningrad University. In

Michigan State University Michigan State University (Michigan State or MSU) is a public university, public Land-grant university, land-grant research university in East Lansing, Michigan, United States. It was founded in 1855 as the Agricultural College of the State o ...

's department of mathematics, he was from 1991 to 1992 a visiting assistant professor, from 1992 to 1994 an assistant professor, from 1994 to 1998 he was an associate professor, and from 1998 to 1999 a full professor. In

Brown University Brown University is a Private university, private Ivy League research university in Providence, Rhode Island, United States. It is the List of colonial colleges, seventh-oldest institution of higher education in the US, founded in 1764 as the ' ...

's department of mathematics, he was from 2000 to 2001 an associate professor and was appointed in 2001 a full professor. He was a

visiting scholar In academia, a visiting scholar, visiting scientist, visiting researcher, visiting fellow, visiting lecturer, or visiting professor is a scholar from an institution who visits a host university to teach, lecture, or perform research on a topic fo ...

in 1990 at the

Mittag-Leffler Institute The Mittag-Leffler Institute (Swedish: Institut Mittag-Leffler) is a mathematical research institute in Sweden. Located in Djursholm, a suburb of Stockholm, it invites scholars to participate in half-year programs in specialized mathematical su ...

, where he worked with Alexandre Megretski of the

KTH Royal Institute of Technology KTH Royal Institute of Technology (), abbreviated KTH, is a Public university, public research university in Stockholm, Sweden. KTH conducts research and education in Institute of technology, engineering and technology and is Sweden's largest te ...

. Treil was in autumn 1998 a visiting professor at

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

's department of electrical engineering and computer science. Treil has done important research in the intersection of

operator theory In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operato ...

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

, and

harmonic analysis Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded do ...

. Much of his research is on problems related to

applied mathematics Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...

, such as

control theory Control theory is a field of control engineering and applied mathematics that deals with the control system, control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the applic ...

, stationary random processes,

signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomograph ...

, and

wavelet A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the n ...

s. His research interest include Hankel operators, Toeplitz operators,

functional model In systems engineering, software engineering, and computer science, a function model or functional model is a structured representation of the Function (engineering), functions (Activity diagram, activities, Task analysis, actions, wikt:process, pr ...

s of operators, spectral decompositions of operators, spectral theory of matrix- and operator-valued functions, the Corona problem, and the interplay between operator theory and

complex geometry In mathematics, complex geometry is the study of geometry, geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of space (mathematics), spaces su ...

. In 1993 Treil was awarded the

Salem Prize The Salem Prize, in memory of Raphael Salem, is awarded each year to young researchers for outstanding contributions to the field of analysis. It is awarded by the School of Mathematics at the Institute for Advanced Study in Princeton and was fou ...

. He wrote several papers with Alexander Volberg and

Fedor Nazarov Fedor (Fedya) L'vovich Nazarov (; born 1967) is a Russian mathematician working in the United States. He has done research in mathematical analysis and its applications, in particular in functional analysis and classical analysis (including harm ...

, who were his colleagues at Michigan State University. Volberg shared the 1988 Salem Prize with

Jean-Christophe Yoccoz Jean-Christophe Yoccoz (29 May 1957 – 3 September 2016) was a French mathematician. He was awarded a Fields Medal in 1994, for his work on dynamical systems. Yoccoz died on 3 September 2016 at the age of 59. Biography Yoccoz attended the Lyc� ...

. Nazarov won the 1999 Salem Prize.

Selected publications

* -- St. Petersburg Math. J., vol. 8, issue 5, 1997, pp. 721–824
paper id 736. mathnet.ru
* (over 350 citations) * (over 350 citations) * * * (over 450 citations
preprint
*

References

External links

mathnet.ru
* (extensive publication list with links to many preprints)

(a textbook for an honors linear algebra course) (See also Linear algebra#Online books.) {{DEFAULTSORT:Treil, Sergei 20th-century Russian mathematicians 21st-century Russian mathematicians 20th-century American mathematicians 21st-century American mathematicians Saint Petersburg State University alumni Michigan State University faculty Brown University faculty Year of birth missing (living people) Living people