For additional information see Joseph Flenner's Personal Page.
Research Interests
My research is focused on interactions between logic and algebra, primarily in model theory. In particular, I have been studying definability in valued fields. The long-term project here would be to try to give something like a characterization of the definable sets of henselian valued fields via elimination of imaginaries relative to structures of leading terms. More recently, I have started looking at the application of the model theory of valued fields to tropical geometry.
I am also interested in arithmetic questions about decidability, including in particular Hilbert's Tenth Problem. One example of a problem here would be to describe definable classes of finitely generated fields.
Selected Publications
Please direct questions and comments to: flenner.1@nd.edu |
