# Fields Academy Shared Graduate Course: Massive C* Algebras

Instructor: Prof. Ilijas Farah

Email: ifarah@yorku.ca

Application Deadline: January 19th, 2021

Lecture Times: Mondays and Fridays | 9:00 am - 10:30 am

Course Dates: January 11th - April 9th, 2021

Course Overview

The route to understanding separable C*-algebras frequently involves a detour via nonseparable C*-algebras, such as the Calkin algebra, the asymptotic sequence algebras, ultrapowers, and ultraproducts. Some basic ideas from logic can be used to analyze these massive C*-algebras. Among other things, we will see that the existence of outer automorphisms of the Calkin algebra depends on the set-theoretic axioms.

## Schedule

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Preliminary analysis of C*-algebras of density character aleph_1, Downward Lowenheim-Skolem Theorem.
Ilijas Farah, York University |

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Ilijas Farah, York University |

09:00 to 10:30 |
Homework 2 discussion and solutions
Ilijas Farah, York University |

09:00 to 10:30 |
The posets PartN and N↑N. Meagre subsets of product spaces.
Ilijas Farah, York University |

09:00 to 10:30 |
The Calkin algebra has outer automorphisms.
Ilijas Farah, York University |

09:00 to 10:30 |
The Calkin algebra has outer automorphisms.
Ilijas Farah, York University |

09:00 to 10:30 |
Ulam-stability of approximate ∗-homomorphisms. Liftings of ∗-homomorphisms between coronas.
Ilijas Farah, York University |

09:00 to 10:30 |
Ulam-stability of approximate ∗-homomorphisms. Liftings of ∗-homomorphisms between coronas.
Ilijas Farah, York University |

09:00 to 10:30 |
All automorphisms of the Calkin algebra are inner.
Ilijas Farah, York University |

09:00 to 10:30 |
All automorphisms of the Calkin algebra are inner.
Ilijas Farah, York University |

09:00 to 10:30 |
All automorphisms of the Calkin algebra are inner (continued).
Ilijas Farah, York University |

09:00 to 10:30 |
All automorphisms of the Calkin algebra are inner (continued).
Ilijas Farah, York University |

09:00 to 10:30 |
Final project presentations.
Ilijas Farah, York University |

09:00 to 10:30 |
Final project presentations.
Ilijas Farah, York University |