Research and Publications

I'm interested in the intersection of model theory and combinatorics. Some topics include $\omega$-categoricity, homogeneity, structural Ramsey theory, tame hereditary classes, and extremal combinatorics. Here is a copy of my research statement.

  1. (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

  2. The lattice of definable equivalence relations in homogeneous $n$-dimensional permutation structures. The Electronic Journal of Combinatorics 23 (2016), no. 4, Paper 44 Journal link

  3. Ramsey expansions of $\Lambda$-ultrametric spaces. (submitted) arXiv link

  4. Homogeneous 3-dimensional permutation structures. The Electronic Journal of Combinatorics 25 (2018), no. 2, Paper 52 Journal link

  5. (with Pierre Simon) The classification of homogeneous finite-dimensional permutation structures. The Electronic Journal of Combinatorics 27 (2020), no. 1, Paper 38 Journal link

  6. $\Lambda$-ultrametric spaces and lattices of equivalence relations. Algebra Universalis. 80 (2019), no.3 arXiv link

  7. The undecidability of joint embedding and joint homomorphism for hereditary graph classes. Discrete Mathematics & Theoretical Computer Science. 21 (2019), no. 2 Journal link

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

  9. (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

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

  11. Monadic stability and growth rates of $\omega$-categorical structures. (To appear in Proceedings of the London Mathematical Society) arXiv link

  12. (with Michael C. Laskowski) Mutual algebraicity and cellularity. (To appear in Archive for Mathematical Logic) arXiv link

  13. (with Michael C. Laskowski) Counting siblings in universal theories. (To appear in Journal of Symbolic Logic) arXiv link

  14. (with Michael C. Laskowski) Worst case expansions of complete theories. (submitted) arXiv link

  15. (with Michael C. Laskowski) Theories admitting congruences over sets and boundedness. (submitted) arXiv 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. (Paper 7) Slides

  2. Homogeneous finite-dimensional permutation structures. (Paper 5) Video Slides

  3. Cellularity and beyond. (Papers 12-13) Video Slides

  4. Characterizations of monadic NIP. (Paper 10) Video Slides

  5. Counting substructures of highly symmetric structures. (Paper 11) Slides