Mathematical Modeling of Biological Systems and of Linguistics
Computer Graphics
Optimization and Electrical Energy
Differential Geometry
Algebra and Algebraic Geometry
Mathematical Economy and Finances
Control Theory
Partial Differential Equations
Operator Algebras and Harmonic Anal.
Combinatorics and Algorithms
Petroleum Sciences
Weather Predictions and Climate
Dynamical Systems
Probability
Topology and Singularities
Mathematical Teaching and Olympiads

Operator Algebras and Harmonic Analysis

Team and Interlocutors

R. Exel

V. Jones (Berkeley), M. Laca (Münster), J. Roberts (Roma), M. Rordam (Copenhagen)

 

Research Topics

The theory of Operator Algebras deals with algebras consisting of operators on Hilbert space. Such algebras occur in several contexts both in pure and applied mathematics. Its study is closely connected to some of the most exciting mathematical advances of the twentieth century, with fundamental contributions to Dynamical Systems, Differential Geometry, Number Theory, Quantum Mechanics and Genetics.

Although one of the youngest areas of Mathematics, having been initiated by von Neumann em 1929, two Fields medals have already been awarded to researchers in this area (Alain Connes in 1983 and Vaughan Jones in 1990).

Research in Operator Algebras in Brazil is mostly conducted with the aim of obtaining applications to Non-commutative Dynamics, including the study of equilibrium states. International contacts, essential to the establishment of a new area of research in Brazil, have been extensive.