Research and Publications

I'm interested in the intersection of model theory and combinatorics. Some topics include tame hereditary classes, structural graph theory, $\omega$-categoricity, homogeneity, structural Ramsey theory, and extremal combinatorics. Here is a copy of my research statement.
My publications can be viewed chronologically on Google Scholar, so below I have indulged that irrepressible human instinct for classification. (I can only aspire to this.)

Monadic dividing lines and hereditary classes (Tame ones)
  1. (with Michael C. Laskowski) Counting siblings in universal theories. Journal of Symbolic Logic 87 (2022) no. 3 arXiv link

  2. (with Michael C. Laskowski) Mutual algebraicity and cellularity. Archive for Mathematical Logic 61 (2022) arXiv link

  3. (with Michael C. Laskowski) Theories with few non-algebraic types over models, and their decompositions. Proceedings of the American Mathematical Society 150 (2022) no. 9, arXiv link

  4. (with Michael C. Laskowski) Worst-case expansions of complete theories. Model Theory 1 (2022) no. 1 Journal link

  5. Monadic stability and growth rates of $\omega$-categorical structures. Proceedings of the London Mathematical Society, 124 (2022), no. 3 arXiv link

  6. (with Michael C. Laskowski) Characterizations of monadic NIP. Transactions of the American Mathematical Society, Series B. 8 (2021), Journal link

  7. (with Michael C. Laskowski) Existential characterizations of monadic NIP. (submitted) arXiv link

  8. (with Anuj Dawar, Ioannis Eleftheriadis, and Aris Papadopoulos) Monadic NIP in monotone classes of relational structures. ICALP 2023 arXiv link

  9. (with Jaroslav Nešetřil, Patrice Ossona de Mendez, and Sebastian Siebertz) On the first-order transduction quasiorder of hereditary classes of graphs. (submitted) arXiv link

  10. (with Jaroslav Nešetřil, Patrice Ossona de Mendez, and Sebastian Siebertz) Decomposition horizons and a characterization of stable hereditary classes of graphs. (submitted) arXiv link

Homogeneous and $\omega$-categorical structures (Innumerable ones) Other (Stray dogs)
  1. The undecidability of joint embedding and joint homomorphism for hereditary graph classes. Discrete Mathematics & Theoretical Computer Science. 21 (2019), no. 2 Journal link

  2. The undecidability of joint embedding for 3-dimensional permutation classes. Discrete Mathematics & Theoretical Computer Science. 22 (2021), no. 2 Journal link

  3. Decidability in geometric grid classes of permutations. (submitted) arXiv link

  4. (with Matthew Kukla (undergraduate co-author)) Logical limit laws for layered permutations and related structures. Enumerative Combinatorics and Applications. 2 (2022), no. 4 Journal link

  5. (with Ertem Esiner, Adilet Kachkeev, Alptekin Küpçü, Öznur Özkasap) FlexDPDP: Flexlist-Based Optimized Dynamic Provable Data Possession. ACM Transactions on Storage 12(4) (2016) 23 ePrint link

Here are slides and videos for some talks I've given.

  1. The undecidability of the joint embedding property for finitely constrainted hereditary graph classes. Slides

  2. Homogeneous finite-dimensional permutation structures. Video Slides

  3. Cellularity and beyond. Video Slides

  4. Characterizations of monadic NIP. Video Slides

  5. Generalizing nowhere dense graph classes. Slides

  6. Counting substructures of highly symmetric structures. Slides