Research

Preprints

  1. Growth of regular partitions 1: Improved bounds for small slicewise VC-dimension, arXiv.
  2. Growth of regular partitions 2: Weak regularity, arXiv.
  3. Growth of regular partitions 3: strong regularity and the vertex partition, arXiv.
  4. Growth of regular partitions 4: strong regularity and the pairs partitions, arXiv.
  5. Higher arity stability and the functional order property, with A. Abd Aldaim and G. Conant, arXiv.
  6. Higher-order generalizations of stability and arithmetic regularity, with J. Wolf. arXiv.
  7. Irregular Triads in 3-uniform hypergraphs, with J. Wolf. arXiv.

See here for a talk on these results.

Publications

  1. An improved bound for regular decompositions of 3-uniform hypergraphs of bounded VC_2-dimension, Model Theory, Vol.2, No.2, 2023. arXiv. Journal.
  2. Quantitative structure of stable sets in finite abelian groups, with J. Wolf, Trans. Amer. Math. Soc. 373 (2020), 3885-3903. arXiv. Journal.
  3. Structure and regularity for subsets of groups with finite VC-dimension, with G. Conant and A. Pillay, J. Eur. Math. Soc., vol. 24, iss. 2 (2022), 583-621.  arXiv.  Journal.
  4. Uniformly bounded arrays and mutually algebraic structures, with M. C. Laskowski, Notre Dame J. Form. Log. 61, no. 2 (2020), 265-282. arXiv. Journal.
  5. Jumps in speeds of hereditary properties in finite relational languages, with M. C. Laskowski, J. Comb. Theory, Series B. vol. 154, (2022), 93-135. arXiv.  Journal.
  6. A group version of stable regularity, with G. Conant and A. Pillay,  Math. Proc. Cambridge Philos. Soc., vol. 168, iss. 2 (2020), 405-413. arXiv. Journal.
  7. Stable arithmetic regularity in the finite-field model, with J. Wolf,  Bull. London Math. Soc. 51 (2018), no. 1, 70-88. arXiv. Journal.
  8. Extremal theory of locally sparse multigraphs, with D. Mubayi, SIDMA, vol. 34, iss. 3 (2020).  arXiv. Journal.
  9. An extremal graph problem with a transcendental solution, with D. Mubayi, Comb. Probab. Comput. 28 (2019), no. 2, 303-324. arXiv. Journal.
  10. VC_l-dimension and the jump to the fastest speed of a hereditary property, Proc. Amer. Math. Soc. 146 (2018), no. 7, 3111-3126. arXiv. Journal.
  11. Structure and enumeration theorems for hereditary properties in finite relational languages, Ann. Pure Appl. Logic 169 (2018), no. 5, 413-449. arXiv. Journal.
  12. On unavoidable induced subgraphs in large prime graphs, with M. Malliaris, J. Graph Theory 88 (2018), no.2, 255-270. arXiv. Journal.
  13. Discrete metric spaces: structure, enumeration, and 0-1 laws, (2016), with D. Mubayi, J. Symb. Logic, 84, Issue 4 (2019), 1293-1325. arXiv. Journal.
  14. Model theoretic properties of the Urysohn sphere, with G. Conant, Ann. Pure Appl. Logic 167 (2016), no. 1, 49-72. arXiv. Journal.