Strong Convergence

Starting 15.10.25, I plan to give a series of informal lectures about the strong convergence phenomenon, mostly following the excellent survey of Ramon van Handel. I will try to make an effort to make the talks accessible to a wide audience. The lectures will be broadcasted on Zoom.

First meeting:

Details: Wednesday Oct 15, Room 155 Ziskind Building, Weizmann Institute, Zoom link.

--- Morning session,10:15 - 12:00: Introduction (Section 1 of [van Handel])

Synopsis: We will introduce the main topic of strong convergence, and mention some of its remarkable applications to almost optimal spectral gaps of graphs and manifolds, C* and von Neumann algebras and random matrix theory.

--- Afternoon session,14:15 - 16:00: What did Haagerup do? ([Haagerup's paper])

Synopsis: We will present U. Haagerup's seminar paper on the free group, in which he discovered the famous Haagerup property, as well as the rapid decay property. We will prove his theorem showing that the free group has a "Fourier-summation" method, which shows the regular representation of the free groups generates a C*-algebra with the approximation property of Banach spaces. This lecture is not strictly prerequisite for later talks.

Second meeting: TBA (probably on Tuesdays in Weizmann, finding a place here is tricky these days...)

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