Sir William Timothy Gowers, is a British mathematician. He is Professeur titulaire of the Combinatorics chair at the Collège de France, and director of research at the University of Cambridge and Fellow of Trinity College, Cambridge. In 1998, he received the Fields Medal for research connecting the fields of functional analysis and combinatorics.
In mathematics, two linear operators are called isospectral or cospectral if they have the same spectrum. Roughly speaking, they are supposed to have the same sets of eigenvalues, when those are counted with multiplicity.
In mathematics, especially in functional analysis, the Tsirelson space is the first example of a Banach space in which neither an ℓ p space nor a c0 space can be embedded. The Tsirelson space is reflexive.
In the field of mathematics known as functional analysis, the invariant subspace problem is a partially unresolved problem asking whether every bounded operator on a complex Banach space sends some non-trivial closed subspace to itself. Many variants of the problem have been solved, by restricting the class of bounded operators considered or by specifying a particular class of Banach spaces. The problem is still open for separable Hilbert spaces.
Jean Louis, baron Bourgain was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic theory and nonlinear partial differential equations from mathematical physics.
To hear the shape of a drum is to infer information about the shape of the drumhead from the sound it makes, i.e., from the list of overtones, via the use of mathematical theory.
The mathematician Irving Kaplansky is notable for proposing numerous conjectures in several branches of mathematics, including a list of ten conjectures on Hopf algebras. They are usually known as Kaplansky's conjectures.
Per H. Enflo is a Swedish mathematician working primarily in functional analysis, a field in which he solved problems that had been considered fundamental. Three of these problems had been open for more than forty years:
Joram Lindenstrauss was an Israeli mathematician working in functional analysis. He was a professor of mathematics at the Einstein Institute of Mathematics.
Beginning in 1974, the fictitious Peter Orno appeared as the author of research papers in mathematics. According to Robert Phelps, the name "P. Orno" is a pseudonym that was inspired by "porno", an abbreviation for "pornography". Orno's short papers have been called "elegant" contributions to functional analysis. Orno's theorem on linear operators is important in the theory of Banach spaces. Research mathematicians have written acknowledgments that have thanked Orno for stimulating discussions and for Orno's generosity in allowing others to publish his results. The Mathematical Association of America's journals have also published more than a dozen problems whose solutions were submitted in the name of Orno.
Peter Balazs is an Austrian mathematician working at the Acoustics Research Institute Vienna of the Austrian Academy of Sciences.
p-adic quantum mechanics is a collection of related research efforts in quantum physics that replace real numbers with p-adic numbers. Historically, this research was inspired by the discovery that the Veneziano amplitude of the open bosonic string, which is calculated using an integral over the real numbers, can be generalized to the p-adic numbers. This observation initiated the study of p-adic string theory. Another approach considers particles in a p-adic potential well, with the goal of finding solutions with smoothly varying complex-valued wave functions. Alternatively, one can consider particles in p-adic potential wells and seek p-adic valued wave functions, in which case the problem of the probabilistic interpretation of the p-adic valued wave function arises. As there does not exist a suitable p-adic Schrödinger equation, path integrals are employed instead. Some one-dimensional systems have been studied by means of the path integral formulation, including the free particle, the particle in a constant field, and the harmonic oscillator.
Mischa Cotlar was a mathematician who started his scientific career in Uruguay and worked most of his life on it in Argentina and Venezuela.
In mathematics, the Kadison–Singer problem, posed in 1959, was a problem in functional analysis about whether certain extensions of certain linear functionals on certain C*-algebras were unique. The uniqueness was proved in 2013.
Gitta Kutyniok is a German applied mathematician known for her research in harmonic analysis, deep learning, compressed sensing, and image processing. She has a Bavarian AI Chair for "Mathematical Foundations of Artificial Intelligence" in the institute of mathematics at the Ludwig Maximilian University of Munich.
George James Minty Jr. was an American mathematician, specializing in mathematical analysis and discrete mathematics. He is known for the Klee–Minty cube, the Browder–Minty theorem, and the Minty-Vitaver theorem on graph coloring.
Alexander "Sandy" Munro Davie is a Scottish mathematician and was the chess champion of Scotland in 1964, 1966, and 1969.
Edward George Effros was an American mathematician, specializing in operator algebras and representation theory. His research included "C*-algebras theory and operator algebras, descriptive set theory, Banach space theory, and quantum information."
Mohammad Sal Moslehian. is an Iranian mathematician and a professor of mathematics at Ferdowsi University of Mashhad, Iran. He is the President of the Iranian Mathematical Society for the period of 2021-2024 and an invited member of the Iranian Academy of Sciences. His Erdős number is 3. He is known for his contribution to the operator and norm inequality. He has developed the orthogonality in Hilbert C*-modules and has significant contributions to operator means. He established noncommutative versions of martingale and maximum inequalities that play an essential role in noncommutative probability spaces. In addition, he has written several expository papers discussing research and education, as well as promoting mathematics.
