In-Person and Online Talk 

Constructing and detecting new exotic phenomena continues to be an important question in four-dimensional topology. We approach this question by considering satellite disks in the four-ball; by choosing appropriate satellite operations, we are able to simplify matters topologically while simultaneously complicating them smoothly. As a result, we produce many new examples of exotic surfaces in the four-ball, as well as many surfaces which are stably exotic, i.e. survive many one-handle stabilizations. 

This draws on joint work with Kyle Hayden, Sungkyung Kang, and JungHwan Park.