Colloquium: Tuesday, May 17, 2 pm. Speaker: Gidi Amir (Bar Ilan). Title: “Liouville groups with very slowly growing harmonic functions”.
A group G has the Liouville property with respect to some generating set S if the only bounded harmonic functions on the Cayley graph of (G,S) are the constant functions. On such Cayley graphs it is interesting to ask how slowly can a non-constant harmonic function grow?
We construct groups with arbitrary slowly growing harmonic functions. More precisely, for any “nice” function f growing slower than log n, we construct a group and a generating set so that there is a non-constant harmonic function growing like f, but any harmonic function asymptotically slower than f must be constant. This is joint work with Gady Kozma.
