Gabriel Conant

Assistant Professor
Department of Mathematics
The Ohio State University

conant.38@osu.edu


CV | Teaching | Publications | Research Notes | PhD Thesis | Expository | 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.

Explore the model theory universe.

My research is partially supported by NSF grant DMS-1855503.

Preprints

Publications

  • Quantitative structure of stable sets in arbitrary finite groups
    Proceedings of the American Mathematical Society 149 (2021) no. 9, 4015-4028 (arXiv, pdf)
  • Pseudofinite groups and VC-dimension, with A. Pillay
    Journal of Mathematical Logic 21 (2021) no. 2 (arXiv, pdf)
  • On finite sets of small tripling or small alternation in arbitrary groups
    Combinatorics, Probability and Computing 29 (2020) no. 6, 807-829 (arXiv, pdf)
  • Weakly minimal groups with a new predicate, with M. C. Laskowski
    Journal of Mathematical Logic 20 (2020) no. 2 (arXiv, pdf)
  • Remarks on generic stability in independent theories, with K. Gannon
    Annals of Pure and Applied Logic 171 (2020), no. 2 (arXiv, pdf)
  • A group version of stable regularity, with A. Pillay and C. Terry
    Mathematical Proceedings of the Cambridge Philosophical Society 168 (2020), 405-413 (arXiv, pdf)
  • Independence in generic incidence structures, with A. Kruckman
    Journal of Symbolic Logic 84 (2019), no. 2, 750-780 (arXiv, pdf)
  • Stability and sparsity in sets of natural numbers
    Israel Journal of Mathematics 230 (2019), no. 1, 471-508 (arXiv, pdf)
  • Definable sets containing productsets in expansions of groups, with U. Andrews and I. Goldbring
    Journal of Group Theory 22 (2019), no. 1, 63-82 (arXiv, pdf)
  • Extending partial isometries of generalized metric spaces
    Fundamenta Mathematicae 244 (2019), no. 1, 1-16 (arXiv, pdf)
  • Multiplicative structure in stable expansions of the group of integers
    Illinois Journal of Mathematics 62 (2018), no. 1-4, 341-364 (arXiv, pdf)
  • On the complexity of finite subgraphs of the curve graph, with E. Bering and J. Gaster
    Osaka Journal of Mathematics 55 (2018), 795-808 (arXiv, pdf)
  • Stable groups and expansions of (Z,+,0), with A. Pillay
    Fundamenta Mathematicae 242 (2018), no. 3, 267-279 (arXiv, pdf)
  • There are no intermediate structures between the group of integers and Presburger arithmetic
    Journal of Symbolic Logic 83 (2018), no. 1, 187-207 (arXiv, pdf)
  • Forking and dividing in Henson graphs
    Notre Dame Journal of Formal Logic 58 (2017), no. 4, 555-566 (arXiv, pdf)
  • An axiomatic approach to free amalgamation
    Journal of Symbolic Logic 82 (2017), no. 2, 648-671 (arXiv, pdf)
  • Neostability in countable homogeneous metric spaces
    Annals of Pure and Applied Logic 168 (2017), no. 7, 1442-1471 (arXiv, pdf)
  • Distance structures for generalized metric spaces
    Annals of Pure and Applied Logic 168 (2017), no. 3, 622-650 (arXiv, pdf)
  • A remark on strict independence relations
    Archive for Mathematical Logic 55 (2016), no. 3-4, 535-544 (arXiv, pdf)
  • Model theoretic properties of the Urysohn sphere, with C. Terry
    Annals of Pure and Applied Logic 167 (2016), no. 1, 49-72 (arXiv, pdf)

Research Notes

  • Forking and dividing with free amalgamation, with A. Kruckman (pdf)
  • Definable types and f-generics in Presburger arithmetic, with S. 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 C. Terry (pdf)
  • Independence, exchange, and strongly minimal theories (pdf)
  • Dividing lines in unstable theories (pdf)

Tools