Gabriel Conant

Lumpkins Postdoctoral Fellow
118 Hayes-Healy
Department of Mathematics
University of Notre Dame

Check out a map of the model theory universe.

CV |  Teaching |  Publications |  Research Notes |  PhD Thesis |  Expository Articles |  Tools

Research Interests

  • Model theory of groups, especially stability and NIP in expansions of groups.
  • Model theory and additive combinatorics, especially arithmetic regularity and sumset configurations.
  • Model theory of homogeneous structures, especially metric spaces and graphs.



  • A group version of stable regularity, with A. Pillay and C. Terry
    accepted to Math. Proc. Camb. Philos. Soc. (arXiv, pdf)
  • Independence in generic incidence structures, with A. Kruckman
    J. Symbolic Logic 84 (2019), no. 2, 750-780 (arXiv, pdf)
  • Multiplicative structure in stable expansions of the group of integers
    llinois J. Math. 62 (2019), no. 1-4, 341-364 (arXiv, pdf)
  • Stability and sparsity in sets of natural numbers
    Israel J. Math. 230 (2019), no. 1, 471-508 (arXiv, pdf)
  • Definable sets containing productsets in expansions of groups, with U. Andrews and I. Goldbring
    J. Group Theory 22 (2019), no. 1, 63-82 (arXiv, pdf)
  • Extending partial isometries of generalized metric spaces
    Fund. Math. 244 (2019), no. 1, 1-16 (arXiv, pdf)
  • On the complexity of finite subgraphs of the curve graph, with E. Bering and J. Gaster
    Osaka J. Math. 55 (2018), 795-808 (arXiv, pdf)
  • Stable groups and expansions of (Z,+,0), with A. Pillay
    Fund. Math. 242 (2018), no. 3, 267-279 (arXiv, pdf)
  • There are no intermediate structures between the group of integers and Presburger arithmetic
    J. Symbolic Logic 83 (2018), no. 1, 187-207 (arXiv, pdf)
  • Forking and dividing in Henson graphs
    Notre Dame J. Formal Logic 58 (2017), no. 4, 555-566 (arXiv, pdf)
  • An axiomatic approach to free amalgamation
    J. Symbolic Logic 82 (2017), no. 2, 648-671 (arXiv, pdf)
  • Neostability in countable homogeneous metric spaces
    Ann. Pure Appl. Logic 168 (2017), no. 7, 1442-1471 (arXiv, pdf)
  • Distance structures for generalized metric spaces
    Ann. Pure Appl. Logic 168 (2017), no. 3, 622-650 (arXiv, pdf)
  • A remark on strict independence relations
    Arch. Math. Logic 55 (2016), no. 3-4, 535-544 (arXiv, pdf)
  • Model theoretic properties of the Urysohn sphere, with C. Terry
    Ann. Pure Appl. Logic 167 (2016), no. 1, 49-72 (arXiv, pdf)

Research Notes

  • Forking and dividing with free amalgamation, with Alex Kruckman (pdf)
  • Definable types and f-generics in Presburger arithmetic, with Somayeh Vojdani (pdf)
  • Properly forking formulas in Urysohn spaces (pdf)

Ph.D. Thesis

Model Theory and Combinatorics of Homogeneous Metric Spaces (pdf, errata)
University of Illinois at Chicago, 2015
Advisor: Dave Marker

Expository Articles

  • "Approximate subgroups of linear groups" in On pseudofinite dimensions by E. Hrushovski
    seminar notes from IHP trimester, spring 2018 (pdf)
  • Ultrametric spaces in continuous logic (pdf)
  • Forking and dividing in continuous logic, with Caroline Terry (pdf)
  • Independence, exchange, and strongly minimal theories (pdf)
  • Dividing lines in unstable theories (pdf)