Research

The focus of my research is computability theory and its applications. Computability theory is the branch of mathematical logic and theoretical computer science which studies the mathematical foundations of computer algorithms and computation.

My work has been particularly focused on applications of computability theory to the domains of algorithmic information theory, symbolic dynamics, and analysis. The enumeration degrees feature prominently in my work; this degree structure captures the computational complexity of streams of data.

Works

• Pointwise complexity of the derivative of a computable function. Archive for Mathematical Logic 60 (2021), 981–994. [doi] [SharedIt]
• Cototal enumeration degrees and their applications to effective mathematics. Proceedings of the American Mathematical Society 146 (2018), 3541–3552. [doi]
• Strong difference randomness and jump domination. Available on request.
• Characterizing the strongly jump-traceable sets via diagonal non-computability. Available on request.