Most of my work is in geometry and topology. To be more specific, I have spent some time on Teichmüller theory (see my papers with Dmitri Gekhtman and Lizhen Ji, below). Here are some slides about my work on isometric submersions of Teichmüller spaces. I am also interested in applications to other fields (not necessarily pure mathematics).
I defended my thesis on February 5th, 2021. It is entitled Some New Directions in Teichmüller Theory. My defense talk was virtual; slides are available here.
- Gekhtman, D., Greenfield, M. Isometric submersions of Teichmüller spaces are forgetful. To appear. Available at arXiv: 1901.02586.
- Greenfield, M., Ji, L. Metrics and compactifications of Teichm\"uller spaces of flat tori. To appear. Available at arXiv: 1903.10655.
- Aidala, C., Carcassi, G., Greenfield, M. Topology and experimental distinguishability. To appear. Available at arXiv: 1708.05492.
- Greenfield, M., Zhang, J. Null preference and the resolution of the topological social choice paradox. Mathematical Social Sciences 93 (2018), 47--51. Available here.
- Greenfield, M. A lower bound for Torelli-K-quasiconformal homogeneity. Geometriae Dedicata 177 (2014), Issue 1, 61-70. Available at arXiv: 1309.2666.
- Greenfield, M., Marcolli, M. and Teh, K., Twisted spectral triples and quantum statistical mechanical systems, p-Adic Numbers Ultrametric Anal. Appl. 6 (2014), no. 2, 81-104. Available at arXiv: 1305.5492.
- Increasing the solar cell power output by coating with transition metal-oxide nanorods. Applied Energy 88 (2011), 4218–-4221. Available here.