William Paul Thurston was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds.
Complex dynamics, or holomorphic dynamics, is the study of dynamical systems obtained by iterating a complex analytic mapping. This article focuses on the case of algebraic dynamics, where a polynomial or rational function is iterated. In geometric terms, that amounts to iterating a mapping from some algebraic variety to itself. The related theory of arithmetic dynamics studies iteration over the rational numbers or the p-adic numbers instead of the complex numbers.
Curtis Tracy McMullen is an American mathematician who is the Cabot Professor of Mathematics at Harvard University. He was awarded the Fields Medal in 1998 for his work in complex dynamics, hyperbolic geometry and Teichmüller theory.
Yakov Grigorevich Sinai is a Russian–American mathematician known for his work on dynamical systems. He contributed to the modern metric theory of dynamical systems and connected the world of deterministic (dynamical) systems with the world of probabilistic (stochastic) systems. He has also worked on mathematical physics and probability theory. His efforts have provided the groundwork for advances in the physical sciences.
In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of "expansion" and "contraction". Anosov systems are a special case of Axiom A systems.
In mathematics, an interval exchange transformation is a kind of dynamical system that generalises circle rotation. The phase space consists of the unit interval, and the transformation acts by cutting the interval into several subintervals, and then permuting these subintervals. They arise naturally in the study of polygonal billiards and in area-preserving flows.
Mitsuhiro Shishikura is a Japanese mathematician working in the field of complex dynamics. He is professor at Kyoto University in Japan.
Smale's problems are a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 and republished in 1999. Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century. Arnold's inspiration came from the list of Hilbert's problems that had been published at the beginning of the 20th century.
Joan Sylvia Lyttle Birman is an American mathematician, specializing in low-dimensional topology. She has made contributions to the study of knots, 3-manifolds, mapping class groups of surfaces, geometric group theory, contact structures and dynamical systems. Birman is research professor emerita at Barnard College, Columbia University, where she has been since 1973.
Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory. Part of the inspiration comes from complex dynamics, the study of the iteration of self-maps of the complex plane or other complex algebraic varieties. Arithmetic dynamics is the study of the number-theoretic properties of integer, rational, p-adic, or algebraic points under repeated application of a polynomial or rational function. A fundamental goal is to describe arithmetic properties in terms of underlying geometric structures.
Karen Vogtmann (born July 13, 1949 in Pittsburg, California) is an American mathematician working primarily in the area of geometric group theory. She is known for having introduced, in a 1986 paper with Marc Culler, an object now known as the Culler–Vogtmann Outer space. The Outer space is a free group analog of the Teichmüller space of a Riemann surface and is particularly useful in the study of the group of outer automorphisms of the free group on n generators, Out(Fn). Vogtmann is a professor of mathematics at Cornell University and the University of Warwick.
Igor Rivin is a Russian-Canadian mathematician, working in various fields of pure and applied mathematics, computer science, and materials science. He was the Regius Professor of Mathematics at the University of St. Andrews from 2015 to 2017, and was the chief research officer at Cryptos Fund until 2019. He is doing research for Edgestream LP, in addition to his academic work.
William A. Veech was the Edgar O. Lovett Professor of Mathematics at Rice University until his death. His research concerned dynamical systems; he is particularly known for his work on interval exchange transformations, and is the namesake of the Veech surface. He died unexpectedly on August 30, 2016 in Houston, Texas.
Manfred Leopold Einsiedler is an Austrian mathematician who studies ergodic theory. He was born in Scheibbs, Austria in 1973.
Jeremy Adam Kahn is an American mathematician. He works on hyperbolic geometry, Riemann surfaces and complex dynamics.
Tan Lei was a mathematician specialising in complex dynamics and functions of complex numbers. She is most well-known for her contributions to the study of the Mandelbrot set and Julia set.
Francis Bonahon is a French mathematician, specializing in low-dimensional topology.
Zhihong "Jeff" Xia is a Chinese-American mathematician.
Shmuel Friedland is an Israeli-American mathematician.
Shen Weixiao is a Chinese mathematician, specializing in dynamical systems.
