Gabriel Conant
Lumpkins Postdoctoral Fellow
118 Hayes-Healy
Department of Mathematics
University of Notre Dame
gconant@nd.edu
Check out a map of the model theory universe.
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.
Preprints
- Weakly minimal groups with a new predicate, with M. C. Laskowski
arXiv 1809.04940, pdf
- On finite sets of small tripling or small alternation in arbitrary groups
arXiv 1806.06022, pdf
- Structure and regularity for subsets of groups with finite VC-dimension, with A. Pillay and C. Terry
arXiv 1802.04246, pdf
- Pseudofinite groups and VC-dimension, with A. Pillay
arXiv 1802.03361, pdf
- A group version of stable regularity, with A. Pillay and C. Terry
arXiv 1710.06309, pdf
- Independence in generic incidence structures, with A. Kruckman
arXiv 1709.09626, pdf
- Multiplicative structure in stable expansions of the group of integers,
arXiv 1704.00105, pdf
- Definable sets containing productsets in expansions of groups, with U. Andrews and I. Goldbring
arXiv 1701.07791, pdf
Publications
- Stability and sparsity in sets of natural numbers
accepted to Israel J. Math. (arXiv, pdf)
- Extending partial isometries of generalized metric spaces
accepted to Fund. Math. (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)