I am a graduate student in my final year at OSU. Roughly, my research interests are centered around functor calculi and related questions and applications. In particular, I like those questions that intersect with aspects of geometry (e.g., questions about general manifold topology and symplectic topology) and homotopy theory (e.g., questions about operads and their algebras and modules).
For instance, there is not much known about Taylor towers in Goodwillie calculus centered away from the basepoint. However, in work joint with John Harper (to be uploaded to the arXiv!) we analyze completion with respect to stabilization— that is, the first polynomial approximation of the identity functor— in the context of retractive operadic algebras in modules over the sphere spectrum, inspired by ideas of functor calculus. Our work builds upon that of Ching and Harper, who studied this in the case where the category of $\mathcal{O}$-algebras is retractive over the basepoint. Similarly, in a recent and ongoing collaboration, joint with Niall Taggart and Kaya Ferendo, we seek to generalize and better understand aspects of Weiss' orthogonal calculus. We have constructed variants of Weiss' orthogonal calculus and we wish to understand how far this can be pushed!
To hear more about any of the above and the other things I've been thinking about recently (in particular, if you have any strong feelings about symplectic geometry or enveloping operads), don't be afraid to reach out by email! My research statement is also available by request.
My email address is available on my OSU department page.