Professor, Mathematics
- PhD, University of Chicago, Mathematics
- MS, University of Chicago, Mathematics
- MASt, University of Cambridge, Mathematics
- BS, California Institute of Technology, Mathematics
Michael Shulman, PhD, joined the faculty at USD in 2013. He teaches various courses in mathematics, and does research in the areas of category theory and algebraic topology.
Scholarly Work
Most recently, Shulman has been involved in developing the new field of homotopy type theory, which combines ideas from algebraic topology with constructive type theory, resulting in a new foundation for mathematics, with intrinsic homotopical content, that can be formally verified by a computer.
Dr. Shulman’s research is in category theory and type theory. Category theory is sometimes called the “mathematics of mathematics”: it studies abstract structures that arise in many different parts of mathematics and their common features. Type theory is a formal system for representing mathematics in a way that a computer can understand; this enables both mathematical proofs and computer programs to be formally verified with near-absolute certainty in their correctness. Recent student projects in these areas have included:
-Conway’s surreal numbers: a formalization in Lean
-New equations for neutral terms: a tutorial implementation in Racket
-Observational Homotopy Type Theory: experiments using Agda rewriting
-The mathematics of adverbs: adjoining adjoints to 2-categories for modal logic
Areas of Interest
Shulman's teaching emphasizes a conceptual understanding of mathematics as a creative and participatory activity, and a skill of logical reasoning.