Current Research Interests
1. Global Equivariant Commutative Orientations: The central notion in chromatic homotopy theory is the complex orientation of a ring spectrum which can be described as the homotopy class of a ring map MU ---> E. An 𝔼_∞-orientation of an 𝔼_∞-ring spectrum is an 𝔼_∞-ring map MU ---> E and Hopkins-Lawson described an obstruction theory for extending a complex orientation to an 𝔼_∞-orientation.
The current goal of my PhD project is to generalize this to a (global) equivariant setting. One ingredient to make this obstruction theory run seems to be an equivariant version of Antolín-Camarena-Barthel's universal property of Thom ring spectra on which I am working.
See here for a poster.
2. Fractured Structure on Condensed Anima (joint with Nima Rasekh): The categorical foundation of condensed mathematics lies in topos theory. This project has grown out of my master's thesis and our goal is to establish formal properties of Carchedi and Lurie's fractured topoi. One possible application is the study of condensed cohomology.
See here for my master's thesis on this topic.