My research is in the area of algebraic topology known as stable homotopy theory, in connection with algebraic K-theory, higher category theory and theoretical computer science. I am particularly interested in showing how certain algebraic structures lead to new and effective computations. For instance, I have shown that model categories fail to accurately represent so-called coalgebraic structures in stable homotopy theory, and hence we need the language of ∞-categories to accurately capture homotopy coherent structures. More recently, I have studied trace methods to compute algebraic K-theory and introduced new variants of topological Hochschild homology. I have also extended my interests to theoretical computer science, applying methods of category theory and coalgebras to study algebraic data type interactions.
Equivariant algebraic K-theory of symmetric monoidal Mackey functors, with Maxine Calle and David Chan, (submitted)
A monoidal Dold-Kan correspondence for comodules, (submitted).
Rigidification of Connective Comodules, (submitted).