Appears in collection : 2022 - T2 - WS2 - Self-similarity of groups, trees and fractals

The subject of this talk will be automorphisms of Cayley graphs. They always contain the translations by the elements of the group, but the automorphism group can be much larger (think of a the standard Cayley graph of free groups). Given a finitely generated group, we will be interested in how and when a careful choice of a generating set can make the automorphism group very small. In particular, I will explain that every finitely generated group admits a Cayley graph with countable automorphism group.

Based on joint works with Paul-Henry Leemann.