I study chromatic stable homotopy theory from the point of view of the geometry of formal groups and p-divisible groups. I'm particularly interested in transchromatic questions: what happens when formal groups change height, and what this tells us about chromatic localizations. I'm also interested in using the analytic geometry of Lubin-Tate space to study the action of the Morava stabilizer group.
I made a short video summary of my current research for the electronic Algebraic Topology Employment Network. You can watch it on Youtube.
Dominic Leon Culver and Paul VanKoughnett, On the K(1)-local homotopy of tmf∧tmf (2019), arXiv:1908.01904.
Piotr Pstrągowski and Paul VanKoughnett, Abstract Goerss-Hopkins-Theory (2019), submitted, arXiv:1904.08881.
My thesis: Localizations of E-theory and Transchromatic Phenomena in Stable Homotopy Theory.