Oberseminar mathematische Logik
Organizers
- Prof. Dr. Peter Koepke
- Dr. Philipp Lücke
Time and location
Tuesdays 10-12 in room N0.003, or by appointment (see below), Endenicher Allee 60.
The participants of the seminar are welcome for coffee and tea in the Hausdorffraum at 10.00 before the talks.
Talks
- 19 June (16.30 -18.00, SR 0.007): Moritz Weber (Saarbrücken) Forcing in operator algebras
In operator algebras, a number of very concrete questions have been „solved" by the use of forcing: A good number of statements are independent from ZFC, and surprisingly, these statements first appeared to be quite „solvable“ to operator algebraists. So, forcing has become a widely accepted tool in operator algebras, mainly by the work of Farah and Weaver, but also by others.
In my talk, I will approach some of the statements from the perspective of a forcing friendly operator algebraist. In particular, I will try to present the main aspects of Farah’s famous Annals paper „All automorphisms of the Calkin algebra are inner“ from 2011, using CH on the one hand and Todorcevic’s Axiom on the other to prove independence from ZFC for the existence of outer automorphisms. Note that the Calkin algebra is the quotient of the algebra of bounded linear operators on a Hilbert space (a kind of infinite dimensional matrices) by the ideal of compact operators (a kind of limits of finite-dimensional matrices). The question is whether or not any *-algebra isomorphism of the Calkin algebra comes from a unitary (the isomorphisms of Hilbert spaces). This question is independent from ZFC. See also the Oberwolfach Workshop Report 13/2010 for further results at the intersection of forcing and operator algebras.