Huy Tran: The continuity of Loewner map

The Loewner map uses a special differential equation that describes a non-crossing curve in the upper half-plane through a real-valued function, called the driving function. One of the main questions in the Loewner theory is to understand how the regularity of the curve depends on the space that the driving function lives. The space can be the Wiener space, where the Brownian motion lives, or Holder spaces. In this talk, we will review these results. Then we will focus on another question: How stable is the Loewner map in these spaces? Interestingly, this question is more difficult. We will present a partial answer to the question in the talk.