Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence.
Stephen Smale is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics faculty of the University of California, Berkeley, where he currently is Professor Emeritus, with research interests in algorithms, numerical analysis and global analysis.
Manuel Blum is a Venezuelan born American computer scientist who received the Turing Award in 1995 "In recognition of his contributions to the foundations of computational complexity theory and its application to cryptography and program checking".
In computability theory, the theory of real computation deals with hypothetical computing machines using infinite-precision real numbers. They are given this name because they operate on the set of real numbers. Within this theory, it is possible to prove interesting statements such as "The complement of the Mandelbrot set is only partially decidable."
Lenore Carol Blum is an American computer scientist and mathematician who has made contributions to the theories of real number computation, cryptography, and pseudorandom number generation. She was a distinguished career professor of computer science at Carnegie Mellon University until 2019 and is currently a professor in residence at the University of California, Berkeley. She is also known for her efforts to increase diversity in mathematics and computer science.
In computational complexity theory, R is the class of decision problems solvable by a Turing machine, which is the set of all recursive languages.
Joseph Frederick Traub was an American computer scientist. He was the Edwin Howard Armstrong Professor of Computer Science at Columbia University and External Professor at the Santa Fe Institute. He held positions at Bell Laboratories, University of Washington, Carnegie Mellon, and Columbia, as well as sabbatical positions at Stanford, Berkeley, Princeton, California Institute of Technology, and Technical University, Munich.
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.
In computation theory, the Blum–Shub–Smale machine, or BSS machine, is a model of computation introduced by Lenore Blum, Michael Shub and Stephen Smale, intended to describe computations over the real numbers. Essentially, a BSS machine is a Random Access Machine with registers that can store arbitrary real numbers and that can compute rational functions over reals in a single time step. It is closely related to the Real RAM model.
In computing, especially computational geometry, a real RAM is a mathematical model of a computer that can compute with exact real numbers instead of the binary fixed point or floating point numbers used by most actual computers. The real RAM was formulated by Michael Ian Shamos in his 1978 Ph.D. dissertation.
Robert Edward "Rufus" Bowen was an internationally known professor in the Department of Mathematics at the University of California, Berkeley, who specialized in dynamical systems theory. Bowen's work dealt primarily with axiom A systems, but the methods he used while exploring topological entropy, symbolic dynamics, ergodic theory, Markov partitions, and invariant measures "have application far beyond the axiom A systems for which they were invented." The Bowen Lectures at the University of California, Berkeley, are given in his honor.
In mathematical logic, computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the form
Morris William Hirsch is an American mathematician, formerly at the University of California, Berkeley.
Richard M. Pollack was an American geometer who spent most of his career at the Courant Institute of Mathematical Sciences at New York University, where he was Professor Emeritus until his death.
Foundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.
Beresford Neill Parlett is an English applied mathematician, specializing in numerical analysis and scientific computation.
Peter Bürgisser is a Swiss mathematician and theoretical computer scientist who deals with algorithmic algebra and algebraic complexity theory.
Complexity and Real Computation is a book on the computational complexity theory of real computation. It studies algorithms whose inputs and outputs are real numbers, using the Blum–Shub–Smale machine as its model of computation. For instance, this theory is capable of addressing a question posed in 1991 by Roger Penrose in The Emperor's New Mind: "is the Mandelbrot set computable?"
Juan Felipe Cucker Farkas is an Uruguayan mathematician and theoretical computer scientist who has done research into the complexity theory of the Blum–Shub–Smale computational model and the complexity of numerical algorithms in linear programming and numerical algebraic geometry.
Anders C. Hansen is a Norwegian mathematician, who is currently a Professor of Mathematics at University of Cambridge, where he is the head of the Applied Functional and Harmonic Analysis group, and also Professor II at the University of Oslo. He works in functional analysis, harmonic analysis (applied), foundations of mathematics (computational), data science and numerical analysis.
