Short Course

Masoud Amini, Tarbiat Modares University
C*-Algebras, von Neumann Algebras and K-Theory

In 1930s, Murray and von Neumann laid down the foundations of a mathematical model for quantum mechanics, known as the theory of rings of operators. Later the theory was devided into two main branches: ‎$‎C^*‎$‎-algebras (topological approach) and von Neumann algebras (measure theoretical approach). The theory has deep interactions with other mathematical areas such as topology, dynamical systems, measured group theory, quantum information, and noncommutative geometry.‎

‎These series of talks are for general audience and could serve as a general introduction to the subject. In the first talk the basics of ‎$‎C^*‎$‎-algebras and some main tools, such as representations and functional calculus are presented. The second talk is devoted to type theory and classification of von Neumann algebras, as well as some recent important conjectures such the Connes embedding and Kirchberg conjectures. The last talk is a general intoduction to K-theory of operator algebras and relations with algebraic topology. A sketch of Elliott's program on the classification of simple nuclear ‎$‎C^*‎$‎-algebras is presented.‎

Date & Time: 
Monday, July 25, 2016, 9:00 - 10:30 & 11:00 - 12:30 & 14:00 - 15:30
Lecture Hall 1, Niavaran Building, IPM