- markjg (at) umich (dot) edu
- Office: East Hall 4852

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 |

- Some ideas from Complex Analysis
- Some more details on the previous topic: More Complex Analysis
- A discussion of Cardinality
- Some first principles of Logic and Set Theory
- Getting started on the LaTeX mathematical typesetting system

Last Updated: April 2017.

I am indebted directly to Angus Chung and transitively to Corey Everlove for assistance in constructing this webpage and for the template code.