# Mathematical Sciences Research Institute

Home » Summer School on Operator Algebras and Noncommutative Geometry

Description A famous theorem of Gelfand states that a space can be recovered from the algebra of continuous complex-valued functions on the space. Other algebras, namely those in which multiplication is not commutative, do not correspond to classical spaces, rather, they stand for noncommutative' or quantum' spaces. Based on this, Alain Connes' noncommutative geometry aims to develop the tools of geometry in the setting where a classical space is replaced by a non-commutative algebra of operators as the object of interest. The summer school aims to expose participants to the classi cation of noncommutative spaces, to the study of their homological and cohomological invariants, and to explore fascinating new connections between their symmetries and long standing problems in number theory. The Summer School will feature three 10-lecture series: 1. The structure of nuclear C*-algebras, by Nate Brown (Penn State) and Andrew Toms (Purdue); 2. KK-theory and the Baum-Connes conjecture, by Heath Emerson (Victoria) and Ralf Meyer (Goettingen); 3. C*-dynamical systems from number theory, by Marcelo Laca (Victoria) and Sergey Neshveyev (Oslo). Additional information can be found on the PIMS page .