My research focuses on Ehrhart theory for various families of lattice simplices. In particular, I am interested in Ehrhart positivity, the algebraic and combinatorial properties of the h*-polynomial, and questions concerning the volume and classification of lattice simplices.
I also have a strong interest in the study of unimodular, flag, and regular triangulations of lattice simplices.
Additionally, I have research experience in symmetric functions, partially ordered sets (posets) and enumerative combinatorics, particularly in the theory of set partitions and Stirling numbers.
Sylvester simplices: Triangulations and Ehrhart-theoretic aspects with Federico Castillo, Martina Juhnke and Germain Poullot.
Unimodular triangulations and Ehrhart theory for two families of Hermite normal form simplices with Justus Bruckamp and Martina Juhnke.
Ehrhart non-positivity and unimodular triangulations for classes of s-lecture hall simplices with Martina Juhnke and Germain Poullot.
Partition Lattice with Limited Block Sizes with István Mező and José L. Ramírez.
Extensions of Set Partitions and Permutations with Victor H. Moll, José L. Ramírez and Diego Villamizar.
Conjuntos parcialmente ordenados y retículos with Rafael Gonzáles D'León.
Partially ordered sets and their Möbius functions with Javier A. Gutiérrez and Bruce Sagan. To appear in the book Algebraic and Geometric Combinatorics (Proceedings of ECCO 2003-2018) by Cambridge University Press (accepted in July 2023).