The UCBA Library’s 3rd Annual Faculty Research Lightning Talks on March 10, 2020 featured four presenters and their discipline-based research projects via short, 15 minute presentations. In our *Meet the Presenters* series, each presenter shares some insights into their research project.

David Freeman| Associate Professor of Mathematics| Math, Physics & Computer Science Department

Presentation: *Geometry from Symmetry*

**Research Project**

My research has been focused on the concept of symmetry. Here I use the word “symmetry” to denote a way to transform an object into itself (e.g. a reflection or rotation). My goal is to understand all possible objects that admit certain types of symmetries.

**Are there any opportunities for cross-disciplinary collaboration with your research? If already cross-disciplinary, are there opportunities to expand it?**

Yes, at least to some extent. I am very interested in the philosophy of mathematics, and I am hoping to eventually contribute to the ongoing debate about the ontology of mathematical objects (such as the ones I study). I am also quite interested in mathematically-inspired artwork. I believe there are many opportunities to express mathematical ideas through visual (and other types of) art.

**What are your next steps with your research?**

My long term goal is to prove a conjecture that has motivated the work I’ve already been doing. This conjecture pertains to the classification of certain mathematical objects that exhibit a high degree of “coarse” symmetry. For all I know the conjecture may end up being false, but I am somewhat optimistic that it is true. I’m not sure if a proof is within reach, but I’m willing to give it a shot. In general, this is the nature of many mathematical research projects: one group of mathematicians will pose a conjecture, and then some other group will prove (or disprove) the conjecture.

**Forthcoming Publication**

David Freeman, Enrico Le Donne. (Forthcoming).** **Toward a quasi-Möbius characterization of Invertible Homogeneous Metric Spaces. *Revista Matemática Iberoamericana.*

*By Lauren Wahman*