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, arXiv:1908.01904 Journal of Homotopy and Related Structures 16, 367-426 (2021).
Piotr Pstrągowski and Paul VanKoughnett, Abstract Goerss-Hopkins-Theory, arXiv:1904.08881, Advances in Mathematics 395, 108098 (2022).
Paul VanKoughnett, Localizations of E-theory and Transchromatic Phenomena in Stable Homotopy Theory, arXiv:2110.13869, submitted.