I am a Ph.D. student in pure mathematics in the Department of Mathematics at the University of Michigan in Ann Arbor. My advisor is Lizhen Ji. I started here in September 2015. I obtained my B.S. in mathematics from Caltech in June 2015. Before that, I lived in Cary, NC, and before that, I lived in Rochester, NY.
Here is my CV.
I am interested in geometry and topology. My favorite types of questions are those in which both geometry and topology play a major role. Specifically, I have been studying Teichmüller spaces and moduli spaces of Riemann surfaces and connections to other geometric objects, such as symmetric spaces, and generalizations. I am also interested in differential geometry, hyperbolic geometry, mapping class groups, and other related objects. Occasionally, I am interested in applications to other fields (not necessarily pure mathematics).
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.
Greenfield, M., Zhang, J. Resolving the topological social choice paradox via the addition of a null preference. In Preparation.
Greenfield, M., Ji, L. A new modular characterization of the hyperbolic plane. In Preparation.
I am not teaching during the 2016-2017 school year. However, I am available to tutor students in many of the undergraduate mathematics courses at U of M, as well as younger students who can come to U of M's central campus. Feel free to email me if interested.
I am serving as the manager and a grad student mentor for the Laboratory of Geometry at Michigan, LOG(M). This is a new program here at U of M in which small teams of motivated undergraduates are set up with a grad student and a postdoc in order to learn more about some interesting topics in geometry, and create some nice visualizations of the concepts. To learn more, visit the LOG(M) website!
|Fall 2015||Math 115: Calculus I (Primary Instructor)|
|Winter 2016||Math 215: Calculus III (Mathematica Lab Instructor)|
|Summer 2013, 2014||Math 0: Transition to Mathematical Proofs (Lead TA, 2014)|
|Spring 2014, 2015||IST 4: Information and Logic|