### My talk at the Weizmann institute (“Dilation theory in action”)

Last week I was invited by Guy Salomon to give a talk at the Group Theory Midrasha at the Weizmann Institute (*Midrasha* is a fancy Hebrew word for *seminar*). Since the seminar there is two hours long, I took the opportunity to try something different, and for the first time in a long while I gave a whiteboard talk, going into the details of the proof of the main result in my paper with Gerhold on perturbation of the Heisenberg commutation relations. The group there at Weizmann is really fantastic with many young and curious (and bright!) students who bombarded me with questions, so the talk was quite alive and I think it was a successful experiment (yesterday I gave a similar talk at the Analysis Seminar at Bar-Ilan University; the crowd was full of strong analysts who also asked great questions, but since I aimed for an hour I got pressed for time, so I think in the end it wasn’t as good. That’s on me, because they actually let me choose whether I want to go for two hours or one, and again I wanted to try something a bit different).

Here is a video recording of the talk.

BTW: You can see that someone in the audience asked me a question that I, embarrassingly, blacked out on: *do strongly commuting (unbounded) operators commute in the sense that there is some dense subspace on which the commutator is defined and equal to zero?* The answer is *yes* and is actually not hard to show with basic semigroup theory techniques. A little trickier is to show that strongly commuting operators have commuting spectral projections – which is an equivalent and perhaps more natural definition of “strong commutation” than the one I gave.