The Stefan problem describes phase transitions, such as ice melting to water. In its simplest formulation, this problem consists of finding the evolution of the temperature off the water when a block of ice is submerged inside.

In this talk, I will first discuss the classical theory for this problem. Then I will present some recent results concerning the fine regularity properties of the interface separating water and ice (the so called "free boundary"). As we shall see, these results provide us with a very refined understanding of the Stefan problem's singularities, and they answer some long-standing open questions in the field.

Registration through the seminar website https://sites.google.com/ncts.ntu.edu.tw/international-gmt-seminar required.