nLab Mike Shulman

Mike Shulman is a Professor at the University of San Diego. His personal web page is here.

Selected writings

On higher inductive types:

• Peter LeFanu Lumsdaine, Mike Shulman, Semantics of higher inductive types, Math. Proc. Camb. Phil. Soc. 169 (2020) 159-208 [arXiv:1705.07088, talk slides pdf, doi:10.1017/S030500411900015X]

On modal type theory:

• Mike Shulman, Semantics of multimodal adjoint type theory (arXiv:2303.02572)

On cohesive homotopy type theory:

• Mike Shulman, Brouwer’s fixed-point theorem in real-cohesive homotopy type theory, Mathematical Structures in Computer Science Vol 28 (6) (2018): 856-941 (arXiv:1509.07584, doi:10.1017/S0960129517000147)

• Mike Shulman, Homotopy type theory: the logic of space, New Spaces in Mathematics: Formal and Conceptual Reflections, ed. Gabriel Catren and Mathieu Anel, Cambridge University Press, 2021 (arXiv:1703.03007, doi:10.1017/9781108854429)

On higher observational type theory:

• Thorsten Altenkirch, Yorgo Chamoun, Ambrus Kaposi, Michael Shulman, Internal parametricity, without an interval (arXiv:2307.06448)

On displayed type theory:

• Astra Kolomatskaia, Michael Shulman, Displayed Type Theory and Semi-Simplicial Types (arXiv:2311.18781)

On univalence and the structure identity principle:

• Benedikt Ahrens, Paige Randall North, Michael Shulman, Dimitris Tsementzis, The Univalence Principle [abs:2102.06275]

On set theory:

• Michael Shulman, Comparing material and structural set theories (arXiv:1808.05204)

On synthetic differential geometry:

• Mike Shulman, Chicago Pizza-Seminar: Synthetic Differential Geometry (pdf)

Talks.

On higher observational type theory:

• Michael Shulman, Towards a Third-Generation HOTT:, talk at Homotopy Type Theory at CMU (2022) [part 1: slides, video; part 2: slides, video; part 3: slides, video]

category: people