Michael Harrison: he/him
Gmail address: mah5044
CV (updated 10/2022)
I am currently a Member at the Institute for Advanced Study, participating in the Special-Year Program on the h-principle. Previously I held postdoctoral positions at Carnegie Mellon, MSRI, and Lehigh University. I completed my Ph.D. at Pennsylvania State University in 2017, advised by Sergei Tabachnikov.
I am interested in a broad range of problems in geometric topology, topological combinatorics, and dynamics. I study functions which satisfy certain differential conditions, for example, embeddings, coupled embeddings, totally nonparallel immersions, and k-regular maps. I have studied the existence of such maps using differential topology and the h-principle, and I have studied obstructions to such maps using topological combinatorics and Borsuk-Ulam type results.
I have also studied great circle fibrations of spheres, line fibrations of Euclidean space, the geodesic complexity of configuration spaces of trees, and billiards in various settings, for example on Finsler manifolds and on spaces of geodesics. See my Research page for detailed explanations!
I subscribe to the Axioms of Federico Ardila-Mantilla:
Axiom 1. Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
Axiom 4. Every student deserves to be treated with dignity and respect.
See here for my own statement on diversity, equity, and inclusion.