The Hakubi Project

   Von Neumann algebra theory was initiated by von Neumann to study quantum mechanics. Roughly speaking, it is a study of matrices of "infinite size". The original motivatoin of this theory is application for physics, but it has also been studied by mathematicians from purely mathematical point of view. In fact, von Neumann algebras have rich structures as mathematical objects and moreover have deep connections with other areas in mathematics, such as K-theory, knot theory, ergodic theory, representation theory, etc. The study of von Neumann algebras, however, is very hard because of "infinite size". It requires lots of technologies from algebra, geometry, and analysis theories.
   In this talk, I introduce von Neumann algebra theory as a mathematical theory. No preliminary knowledge is required. I will mainly focus on definition and difficulty of von Neumann algebras as well as basic problems of this theory.