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.
Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical systems. The notion of deterministic dynamical systems assumes that the equations determining the dynamics do not contain any random perturbations, noise, etc. Thus, the statistics with which we are concerned are properties of the dynamics.
In mathematics, specifically functional analysis, Mercer's theorem is a representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in, is one of the most notable results of the work of James Mercer (1883–1932). It is an important theoretical tool in the theory of integral equations; it is used in the Hilbert space theory of stochastic processes, for example the Karhunen–Loève theorem; and it is also used in the reproducing kernel Hilbert space theory where it characterizes a symmetric positive-definite kernel as a reproducing kernel.
Grigory Aleksandrovich Margulis is a Russian-American mathematician known for his work on lattices in Lie groups, and the introduction of methods from ergodic theory into diophantine approximation. He was awarded a Fields Medal in 1978, a Wolf Prize in Mathematics in 2005, and an Abel Prize in 2020, becoming the fifth mathematician to receive the three prizes. In 1991, he joined the faculty of Yale University, where he is currently the Erastus L. De Forest Professor of Mathematics.
Joachim "Jim" Lambek was a Canadian mathematician. He was Peter Redpath Emeritus Professor of Pure Mathematics at McGill University, where he earned his PhD degree in 1950 with Hans Zassenhaus as advisor.
Yuri Vladimirovich Linnik was a Soviet mathematician active in number theory, probability theory and mathematical statistics.
Hillel "Harry" Furstenberg is a German-born American-Israeli mathematician and professor emeritus at the Hebrew University of Jerusalem. He is a member of the Israel Academy of Sciences and Humanities and U.S. National Academy of Sciences and a laureate of the Abel Prize and the Wolf Prize in Mathematics. He is known for his application of probability theory and ergodic theory methods to other areas of mathematics, including number theory and Lie groups.
Tonny Albert Springer was a mathematician at Utrecht University who worked on linear algebraic groups, Hecke algebras, complex reflection groups, and who introduced Springer representations and the Springer resolution.
Rostislav Ivanovich Grigorchuk is a mathematician working in different areas of mathematics including group theory, dynamical systems, geometry and computer science. He holds the rank of Distinguished Professor in the Mathematics Department of Texas A&M University. Grigorchuk is particularly well known for having constructed, in a 1984 paper, the first example of a finitely generated group of intermediate growth, thus answering an important problem posed by John Milnor in 1968. This group is now known as the Grigorchuk group and it is one of the important objects studied in geometric group theory, particularly in the study of branch groups, automaton groups and iterated monodromy groups. Grigorchuk is one of the pioneers of asymptotic group theory as well as of the theory of dynamically defined groups. He introduced the notion of branch groups and developed the foundations of the related theory. Grigorchuk, together with his collaborators and students, initiated the theory of groups generated by finite Mealy type automata, interpreted them as groups of fractal type, developed the theory of groups acting on rooted trees, and found numerous applications of these groups in various fields of mathematics including functional analysis, topology, spectral graph theory, dynamical systems and ergodic theory.
Kalyanapuram Rangachari Parthasarathy was an Indian statistician who was professor emeritus at the Indian Statistical Institute and a pioneer of quantum stochastic calculus. Parthasarathy was the recipient of the Shanti Swarup Bhatnagar Prize for Science and Technology in Mathematical Science in 1977 and the TWAS Prize in 1996.
Toshikazu Sunada is a Japanese mathematician and author of many books and essays on mathematics and mathematical sciences. He is professor emeritus of both Meiji University and Tohoku University. He is also distinguished professor of emeritus at Meiji in recognition of achievement over the course of an academic career. Before he joined Meiji University in 2003, he was professor of mathematics at Nagoya University (1988–1991), at the University of Tokyo (1991–1993), and at Tohoku University (1993–2003). Sunada was involved in the creation of the School of Interdisciplinary Mathematical Sciences at Meiji University and is its first dean (2013–2017). Since 2019, he is President of Mathematics Education Society of Japan.
Mahendra G. Nadkarni is a professor emeritus at University of Mumbai. Nadkarni obtained his Ph.D. in mathematics from Brown University, the US in 1964 for his work on Ergodic theory. His research interests include Ergodic Theory, Harmonic Analysis, and Probability Theory.
Michael Lin is an Israeli mathematician, who has published scientific articles in the field of probability concentrating on Markov chains and ergodic theory. He serves as professor emeritus at the Department of Mathematics in Ben-Gurion University of the Negev (BGU). Additionally, he is a member of the academic board and serves as the academic coordinator at Achva Academic College.
Wolfgang Krieger is a German mathematician, specializing in analysis.
Mark Lee Green is an American mathematician, who does research in commutative algebra, algebraic geometry, Hodge theory, differential geometry, and the theory of several complex variables. He is known for Green's Conjecture on syzygies of canonical curves.
Rabindra Nath Bhattacharya is a mathematician/statistician at the University of Arizona. He works in the fields of probability theory and theoretical statistics where he has made fundamental contributions to long-standing problems in both areas. Most notable are (1) his solution to the multidimensional rate of convergence problem for the central limit theorem in his Ph.D. thesis published in the Bulletin of the American Mathematical Society and further elaborated in a research monograph written jointly with R. Ranga Rao and (2) the solution of the validity of the formal Edgeworth expansion in collaboration with J.K. Ghosh in 1978. He has also contributed significantly to the theory and application of Markov processes, including numerous co-authored papers on problems in groundwater hydrology with Vijay K. Gupta, and in economics with Mukul Majumdar. Most recently his research has focused on nonparametric statistical inference on manifolds and its applications. He is a co-author of three graduate texts and four research monographs. A comprehensive selection of Bhattacharya's work is available in a special 2016 Contemporary Mathematicians volume published by Birkhäuser. He is married to Bithika Gouri Bhattacharya, with a daughter, a son, and four grandchildren.
Thomas Ward is a British mathematician who works in ergodic theory and dynamical systems and its relations to number theory.
François Ledrappier is a French mathematician.
Klaus Wilhelm Roggenkamp was a German mathematician, specializing in algebra.
