\nPresentation:\u202fGeometry from Symmetry<\/i><\/p>\n
![\"David](\"https:\/\/libapps.libraries.uc.edu\/liblog\/wp-content\/uploads\/2020\/04\/3freemanpresentation.jpg\")
<\/a>David Freeman discusses his research.<\/p><\/div>\n
Research Project<\/b>
\nMy research has been focused on the concept of symmetry. Here I use the word \u201csymmetry\u201d 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.<\/p>\n
Are there any opportunities for cross-disciplinary collaboration with your research? If already cross-disciplinary, are there opportunities to expand it?<\/b>
\nYes, 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\u202fthere\u202fare many opportunities to express mathematical ideas through visual (and other types of) art.<\/p>\n
What are your next steps with your research?<\/b>
\nMy long term goal is to prove a conjecture that has motivated the work I\u2019ve already been doing. This conjecture pertains to the classification of certain mathematical objects that exhibit a high degree of \u201ccoarse\u201d symmetry. For all I know the conjecture may end up being false, but I am somewhat optimistic that it is true. I\u2019m not sure if a proof is within reach, but I\u2019m 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.<\/p>\n
Forthcoming Publication<\/b><\/p>\n
David Freeman, Enrico Le Donne.\u202f(Forthcoming).\u202f<\/b>Toward a quasi-M\u00f6bius characterization of Invertible Homogeneous Metric Spaces<\/a>.\u202fRevista\u202fMatem\u00e1tica\u202fIberoamericana.<\/i><\/p>\n <\/p>\n By Lauren Wahman<\/em><\/p>\n","protected":false},"excerpt":{"rendered":" The UCBA Library\u2019s\u202f3rd Annual Faculty Research Lightning Talks\u202fon March 10, 2020 featured\u202ffour presenters and their discipline-based research projects via short,\u00a015 minute\u00a0presentations. In our\u202fMeet the Presenters\u202fseries, each presenter shares some insights into their research project. David Freeman| Associate Professor\u00a0of Mathematics| Math, … Continue reading