# Gabriel Conant

#### Lumpkins Postdoctoral Fellow

Ph.D. in Pure Mathematics, University of Illinois, Chicago, IL, 2015

MS in Pure Mathematics, University of Illinois, Chicago, IL, 2010

BA in Mathematics, Colgate University, Hamilton, NY, 2008

Email: gconant@nd.edu

Office: 118 Hayes Healy Hall

Phone: (574) 631-6505

Fax: (574) 631-6579

For additional information see Gabriel Conant’s Personal Page.

**Research Interests**

My research focuses on model theory and its interactions with number theory and combinatorics. I am especially interested in the relationship between model theoretically well-behaved (e.g. stable or NIP) expansions of the group of integers, and the structure of definable sets in such expansions. This opens up many connections to combinatorial number theory, including sumset phenomena in sets of integers, and solutions to linear equations in finitely generated multiplicative semigroups. This research also extends to well-behaved expansions of more general groups (especially abelian groups and amenable groups).

I also study the model theory of homogeneous structures, especially homogeneous graphs and metric spaces (e.g. the random graph, the generic triangle-free graph, and the Urysohn space). These structures form a rich and diverse class in the landscape of model theory, and this area of research as applications to combinatorics and asymptotic behavior of finite structures.

**Selected Publications**

- "Stability and sparsity in sets of natural numbers", submitted, arXiv:1701.01387.
- "There are no intermediate structures between the group of integers and Presburger arithmetic", Journal of Symbolic Logic, to appear.
- "Stable groups and expansions of (Z,+,0)" (with Anand Pillay), Fundamenta Mathematicae, to appear.
- "An axiomatic approach to free amalgamation", Journal of Symbolic Logic 82 no. 2, 2017.
- "Neostability in countable homogeneous metric spaces", Annals of Pure and Applied Logic 168 no.7, 2017.

Please direct questions and comments to: gconant@nd.edu