George Pólya was a Hungarian-American mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. He is also noted for his work in heuristics and mathematics education. He has been described as one of The Martians, an informal category which included one of his most famous students at ETH Zurich, John von Neumann.
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 the real line or by Fourier series for periodic functions. Generalizing these transforms to other domains is generally called Fourier analysis, although the term is sometimes used interchangeably with harmonic analysis. Harmonic analysis has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis and neuroscience.
Antoni Zygmund was a Polish mathematician. He worked mostly in the area of mathematical analysis, including especially harmonic analysis, and he is considered one of the greatest analysts of the 20th century. Zygmund was responsible for creating the Chicago school of mathematical analysis together with his doctoral student Alberto Calderón, for which he was awarded the National Medal of Science in 1986.
Elias Menachem Stein was an American mathematician who was a leading figure in the field of harmonic analysis. He was the Albert Baldwin Dod Professor of Mathematics, Emeritus, at Princeton University, where he was a faculty member from 1963 until his death in 2018.
Charles Louis Fefferman is an American mathematician at Princeton University, where he is currently the Herbert E. Jones, Jr. '43 University Professor of Mathematics. He was awarded the Fields Medal in 1978 for his contributions to mathematical analysis.
Terence Chi-Shen Tao is an Australian mathematician who is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory.
Arnaud Denjoy was a French mathematician.
Hugh Lowell Montgomery is an American mathematician, working in the fields of analytic number theory and mathematical analysis. As a Marshall scholar, Montgomery earned his Ph.D. from the University of Cambridge. For many years, Montgomery has been teaching at the University of Michigan.
In mathematics, geometric measure theory (GMT) is the study of geometric properties of sets through measure theory. It allows mathematicians to extend tools from differential geometry to a much larger class of surfaces that are not necessarily smooth.
Leon Melvyn Simon, born in 1945, is a Leroy P. Steele Prize and Bôcher Prize-winning mathematician, known for deep contributions to the fields of geometric analysis, geometric measure theory, and partial differential equations. He is currently Professor Emeritus in the Mathematics Department at Stanford University.
Fedor (Fedya) L'vovich Nazarov 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.
The Hausdorff−Young inequality is a foundational result in the mathematical field of Fourier analysis. As a statement about Fourier series, it was discovered by William Henry Young and extended by Hausdorff. It is now typically understood as a rather direct corollary of the Plancherel theorem, found in 1910, in combination with the Riesz-Thorin theorem, originally discovered by Marcel Riesz in 1927. With this machinery, it readily admits several generalizations, including to multidimensional Fourier series and to the Fourier transform on the real line, Euclidean spaces, as well as more general spaces. With these extensions, it is one of the best-known results of Fourier analysis, appearing in nearly every introductory graduate-level textbook on the subject.
Audrey Anne Terras is an American mathematician who works primarily in number theory. Her research has focused on quantum chaos and on various types of zeta functions.
Donald Lyman Burkholder was an American mathematician known for his contributions to probability theory, particularly the theory of martingales. The Burkholder–Davis–Gundy inequality is co-named after him. Burkholder spent most of his professional career as a professor in the Department of Mathematics of the University of Illinois at Urbana-Champaign. After his retirement in 1998, Donald Burkholder remained a professor emeritus in the Department of Mathematics of the University of Illinois at Urbana-Champaign and a CAS Professor Emeritus of Mathematics at the Center for Advanced Study, University of Illinois at Urbana-Champaign. He was a member of the U.S. National Academy of Sciences and a fellow of the American Mathematical Society.
Gilles I. Pisier is a professor of mathematics at the Pierre and Marie Curie University and a distinguished professor and A.G. and M.E. Owen Chair of Mathematics at the Texas A&M University. He is known for his contributions to several fields of mathematics, including functional analysis, probability theory, harmonic analysis, and operator theory. He has also made fundamental contributions to the theory of C*-algebras. Gilles is the younger brother of French actress Marie-France Pisier.
Alfred S. Posamentier is an American educator and a lead commentator on American math and science education, regularly contributing to The New York Times and other news publications. He has created original math and science curricula, emphasized the need for increased math and science funding, promulgated criteria by which to select math and science educators, advocated the importance of involving parents in K-12 math and science education, and provided myriad curricular solutions for teaching critical thinking in math.
Michael John Dorff is a mathematician at Brigham Young University known for his work in undergraduate research, promoting careers in math, popularizing mathematics, and harmonic mappings.
Francis Michael Christ is an American mathematician and professor at University of California, Berkeley, specializing in harmonic analysis, partial differential equations, and several complex variables. He is known for the Christ–Kiselev maximal inequality.
Gregory Beylkin is a Russian–American mathematician.
SergeiViktorovich Bochkarev is a Soviet and Russian mathematician.
