Mitchell Riley

Postdoctoral Associate Affiliation: NYU Abu Dhabi
Education: BA University of Queensland; MA Western University; PhD Wesleyan University

Research Areas: Homotopy Theory; Type Theory; Modal Logic

Mitchell Riley is a mathematician and computer scientist studying Homotopy Type Theory and its various extensions. His thesis work focused on one such extension: adding linear type formers and combining linear and dependent types in a novel way. This allows type theoretic ideas to be brought to bear on stable homotopy theory, letting us deal with (for example) cohomology in a completely synthetic way.

At the Center for Quantum and Topological Systems, he hopes to apply these techniques to the semantics envisioned by Hisham Sati and Urs Schreiber for their TED-K project. The long-term goal is to find ways to systematically produce internal languages for higher categories, but this remains a work in progress with his collaborators.

He encourages any undergraduate with a bent on mathematics and programming to look into HoTT. The original (and free!) HoTT book is still a good place to start.