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Research and Publications

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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 Michael C. Laskowski) Indiscernibles in monadically NIP theories. (submitted) arXiv link


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


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


11. (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)

• Classification (Those drawn with a very fine camel-hair brush)
  1. 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
  
  
  2. Homogeneous 3-dimensional permutation structures. The Electronic Journal of Combinatorics 25 (2018), no. 2, Paper 52 Journal link
  
  
  3. (with Pierre Simon) The classification of homogeneous finite-dimensional permutation structures. The Electronic Journal of Combinatorics 27 (2020), no. 1, Paper 38 Journal link
  
  
  4. $\Lambda$-ultrametric spaces and lattices of equivalence relations. Algebra Universalis. 80 (2019), no.3 arXiv link
  
  
• Ramsey theory and other combinatorics (Those included in this classification)
  1. Ramsey expansions of $\Lambda$-ultrametric spaces. (To appear in European Journal of Combinatorics) arXiv link
  
  
  2. (with David Chodounský, Noé de Rancourt, Jan Hubička, Jamal Kawach, and Matěj Konečný) Big Ramsey degrees and infinite languages. Advances in Combinatorics. August (2024) Journal link
  
  
  3. (with Andrés Aranda, David Chodounský, Jan Hubička, Matěj Konečný, Jaroslav Nešetřil, and Andy Zucker) Type-respecting amalgamation and big Ramsey degrees. arXiv link
  
  
  4. (with Colin Jahel and Paolo Marimon) When invariance implies exchangeability (and applications to invariant Keisler measures). arXiv link
  
  

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. (To appear in Proceedings of the American Mathematical Society) 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