Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a sequence of random variables in a probability space, where the index of the sequence often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.
William "Vilim" Feller, born Vilibald Srećko Feller, was a Croatian–American mathematician specializing in probability theory.
In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some mathematical space.
In mathematics, the isoperimetric dimension of a manifold is a notion of dimension that tries to capture how the large-scale behavior of the manifold resembles that of a Euclidean space.
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially.
Eugene Borisovich Dynkin was a Soviet and American mathematician. He made contributions to the fields of probability and algebra, especially semisimple Lie groups, Lie algebras, and Markov processes. The Dynkin diagram, the Dynkin system, and Dynkin's lemma are named after him.
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.
Harry Kesten was a Jewish American mathematician best known for his work in probability, most notably on random walks on groups and graphs, random matrices, branching processes, and percolation theory.
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.
Murray Rosenblatt was a statistician specializing in time series analysis who was a professor of mathematics at the University of California, San Diego. He received his Ph.D. at Cornell University. He was also a recipient of a Guggenheim Fellowship, in 1965, and was a member of the National Academy of Sciences. He wrote about 140 research articles, 4 books, and co-edited 6 books.
Yuval Peres is an Israeli mathematician best known for his research in probability theory, ergodic theory, mathematical analysis, theoretical computer science, and in particular for topics such as fractals and Hausdorff measure, random walks, Brownian motion, percolation and Markov chain mixing times. Peres has been accused of sexual harassment by several female scientists.
Nicholas Theodore Varopoulos is a Greek mathematician, who works on harmonic analysis and especially analysis on Lie groups.
Yves Le Jan is a French mathematician working in Probability theory and Stochastic processes.
Maria (Masha) Gordina is a Russian-American mathematician. She is a professor of mathematics at the University of Connecticut. Her research is at the interface between stochastic analysis, differential geometry, and functional analysis, including the study of heat kernels on infinite-dimensional groups.
Stanislav Alexeyevich Molchanov is a Soviet and American mathematician.
Jesper Møller is a Danish mathematician.
Evarist Giné-Masdéu, or simply Evarist Giné, was a Catalan mathematician and statistician. He is known for his pioneering works in probability in Banach spaces, empirical process theory, U-statistics and processes, and nonparametric statistics.
Tianyi Zheng is a Chinese-American mathematician specializing in geometric group theory and probability theory, including the theory of random walks and harmonic functions on groups. She is a professor of mathematics at the University of California, San Diego.
