Rocky Mountain Mathematics Consortium Summer School: The Structure of C*-Algebras

This award provides funding to help defray the expenses of participants in the 'Rocky Mountain Mathematics Consortium Summer School: The Structure of C*-Algebras' that will be held from June 1-5, 2015, on the campus of the University of Wyoming. Operator algebras were introduced by John von Neumann and his collaborator Murray during the 1930's, when mathematicians and physicists began the development of a rigorous description of matter on the atomic scale. The physical theory developed for that description was quantum theory. Mathematically, the possible configurations or states of matter (an electron moving around an atom, for example) are described by certain vector spaces. Performing an experiment on the physical system corresponds mathematically to applying an operator to the vector space of possible states. The collection of such operators is described mathematically as an algebra of operators. Nowadays, the study of operator algebras has become an important mathematical pursuit with applications to many other branches of mathematics and theoretical physics. The study of operator algebra itself also has been developed into several closely related subareas, of which one is structural investigation of the important class called C*-algebras. The classification of C*-algebras has developed rapidly in the past few years, with several exciting results. One goal of this summer school is to pull together these recent results to get a clear picture of the current status of the classification of C*-algebras.

The Rocky Mountain Mathematics Consortium (RMMC) has run a summer school, in which topics vary widely from year to year, for over thirty years. The theme of the 2015 installment in the series is the structure of C*-algebras. The set of topics includes the following: von Neumann algebra techniques in the classification of C*-algebras; an introduction to the K-theory of operator algebras; and higher-rank graph C*-algebras. The event's lecturers include four of the world's leading authorities on C*-algebras: George Elliott, Guihua Gong, Yasuhiko Sato, and Alex Kumjian. The choice of topic was motivated by the secondary purpose of the activity; namely, to prepare the summer school's participants, especially the junior ones, for the regional conference sponsored by the Conference Board of the Mathematical Sciences (CBMS) that will follow it during the second week of June and that has as its focus the so-called basic homotopy lemmas and the asymptotic uniqueness theorem, one of the key ingredients in the recent breakthroughs in the classification of C*-algebras.

Summer school web site: http://www.uwyo.edu/math/additional-learning-opportunities/rmmc-summer-school/