I'm interested in the intersection of model theory and combinatorics. My research thus far has focused on $\omega$-categoricity, homogeneity, and structural Ramsey theory.
| 1. Samuel Braunfeld, 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. Samuel Braunfeld, Ramsey Expansions of $\Lambda$-Ultrametric Spaces. (Submitted to the European Journal of Combinatorics.) arXiv link |
| 3. Samuel Braunfeld, Homogeneous 3-Dimensional Permutation Structures. The Electronic Journal of Combinatorics 25 (2018), no. 2, Paper 52 Journal link |
| 4. Samuel Braunfeld, Pierre Simon, The classification of homogeneous finite-dimensional permutation structures. arXiv link |
The results from the first three papers above, as well as material around the undecidability of the joint embedding property, appear in my thesis Infinite Limits of Finite-Dimensional Permutation Structures, and their Automorphism Groups: Between Model Theory and Combinatorics. arXiv link