# Mathematics Colloquia and Seminars

### Non-uniqueness for specifications in $\ell^{2+\epsilon}$
Keane, Berbee and others have studied the question of which specifications (aka $g$-functions) admit unique Gibbs measure. Bramson and Kalikow contructed the first example of a regular and continuous specification which admits multiple measures. For every $p>2$, we contruct a regular and continuous specification, whose variation is in $\ell^p$, that admits multiple Gibbs measures. This shows that a recent condition of Oberg and Johansson is tight. Based on joint work with Christopher Hoffman and Vlada Sidoravicius.