The half-space directed polymer is a variant of directed polymer that studies how polymers behave in the presence of an attractive wall. Depending on the strength of the boundary, the polymers are expected to have two distinct phases: the bound phase and the unbound phase. In this talk, I will focus on the half-space polymer model with log-gamma weights which makes the model integrable. I will describe our results in the unbound phase where we obtain KPZ exponents and in the bound phase where we obtain stochastic boundedness of the endpoint. Our proof proceeds by constructing the half-space log-gamma line ensemble which has a novel feature of attraction/repulsion at the boundaries. Based on two joint works: one with Guillaume Barraquand and Ivan Corwin, and one with Weitao Zhu.
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