You can find a short 10-minute video on my research here, and a copy of my research statement here.

One of the core aims of my dissertation work is to extend Blumberg and Hill’s \(\mathbb{N}_\infty\)-operad theory, which is an extension of non-equivariant \(\mathbb{E}_\infty\)-operad theory that includes notions of norms in a highly structured way. The importance of this theory is that it provides an overarching framework for norm maps, which in recent years has shown to be integral to the study of equivariant spectra - starting with the Hill-Hopkins-Ravenel solution to the Kervaire Invariant One Problem. However, the extension of \(\mathbb{E}_k\)-operads in this direction is not yet clear and clearing this up is the central goal of my research. The ultimate hope of such an extension is that it will lead to a better understanding of multiplicative objects that appear in equivariant stable homotopy theory, obstructions to such objects, and in practice, help with further computations in equivariant homotopy theory.