Title: Partition functions for directed polymers in the subcritical and critical regimes
Abstract: We consider a model of directed polymers in random environments, which is the discrete analogue of the (multiplicative) stochastic heat equation. We focus on the critical two dimensional setup, and study large moments and maxima of the partition function in the subcritical regime, where we exhibit links with branching random walk with time-varying profiles. If time permits, I will report on recent advance in the understanding of the 
critical regime. (Joint work with Clement Cosco and Shuta Nakajima).