##### Department of Mathematics,

University of California San Diego

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### Math 211A: Seminar in Algebra

## Professor Nicolas Monod

#### EPFL

## The fixed-point property and piecewise-projective transformations of the line

##### Abstract:

We describe a new and elementary proof of the fact that many groups of piecewise-projective transformation of the line are non-amenable by constructing an explicit action without fixed points. One the one hand, such groups provide explicit counter-examples to the Day-von Neumann problem. On the other hand, they illustrate that we can distinguish many "layers" of relative non-amenability between nested subgroups.

Adrian Ioana, Alireza Golsefidy

### November 18, 2024

### 3:00 PM

APM 7321

Research Areas

Algebra Representation Theory****************************