Explore three intriguing problems related to univalent functions in model spaces in this 54-minute lecture by Konstantin Fedorovskiy from Lomonosov Moscow State University. Delivered as part of the Focus Program on Analytic Function Spaces and their Applications at the Fields Institute, delve into new linear domains and understand their significance. Examine the concept of observed continuation and learn about the characterization of domains. Discover a key theorem and its proof, along with insights into the nonrectifier and the house of dimension. Gain historical context through a concluding remark, enhancing your understanding of this complex mathematical topic.