The adsorption phase transition of a polymer to an attractive hard wall is a well-known phenomenon, and has been studied extensively in the mathematics literature: if the attraction intensity to the wall is larger than some critical value, the polymer gets localized in the vicinity of the wall, otherwise it wanders away. In this talk we additionally consider that the polymer is dipped in a poor solvent, with which it interacts repulsively. If the repulsion intensity is large, the polymer folds over on itself into a compact globule, minimizing its
interactions with the solvent. We prove that in this "collapsed" regime, the polymer still undergoes the aforementioned adsorption transition. However, only the outter, bottommost layer of the globule may adhere to the wall: therefore this is not a proper phase transition, and does not appear in the free energy; this phenomenon is called a "surface transition", and is proven by deriving sharp asymptotics of the partition function of this model.