Logarithmic and tropical jacobian: examples and applications

Many degeneration problems have nice answers in the world of log geometry: for example, the Tate curve degenerates to a canonical "log elliptic curve". 'After a brief recap on log schemes, I'll explain the notions of logarithmic and tropical jacobian of a log curve, recently introduced by Molcho and Wise, with the help of examples. If time permits I'll discuss how to construct smooth separated models of the jacobian starting from the log jacobian.