I'm really interested in equivariant algebra: the study of Mackey, Green, and Tambara functors (which are analogues of modules and rings). These originally arose in the context of algebra, although they turn out to arise very naturally in equivariant homotopy theory. A great source of problems in this area is the following: take your favorite commutative algebra textbook, flip to a random page, and try to state and prove analogues of everything you see in equivariant algebra. For example, my UChicago REU student Emory Sun just proved a Tambara functor version of the Hilbert basis theorem!

Besides algebra, I'm also broadly interested in homotopy theory. For example: Balmer spectrum computations; all kinds of orientations; THH, TC, algebraic K-theory, and trace methods; and equivariant analogues of chromatically important spectra like Brown-Peterson spectra, Morava K-theory, and Lubin-Tate spectra.