Complex curves through a contact lens

Kyle Hayden (Boston College)
Every four-dimensional Stein domain has a height function whose regular level sets are contact three-manifolds. Complex curves in the Stein domain can then be studied via their intersection with these contact level sets, where we can comfortably apply three-dimensional tools. We use this perspective to characterize the links in Stein-fillable contact manifolds that bound complex curves in their Stein fillings. (Some of this is joint work with Baykur, Etnyre, Hedden, Kawamuro, and Van Horn-Morris.)