### Property T for bornological groups - note unusual time

Analysis and Geometry Seminar

29th September 2022, 4:15 pm – 5:15 pm

Fry Building, 2.04

In a joint work with Jeroen Winkel, we study fixed-point properties for groups equipped with a left-invariant coarse structure, which we call bornological groups. The first case of interest are locally compact groups. For them, we show that property T is a "coarse property", namely that it is equivalent to a stronger form of property T where no continuity assumption is required on the representation. Another class of interesting bornological groups arise in the study of box spaces. It consists of a certain (large) group coming naturally both with a topology and a coarse structure. We show that both property T and coarse property T for this group are naturally characterized in terms of geometric properties of the box space.

Note unusual seminar time.

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