- Detecting and precluding toricity in reaction network theory
- Generalized polyhedral homotopies and tropical steady state bounds
- Computational and real algebraic geometry: Gröbner bases and comprehensive Gröbner systems; toric geometry; tropical geometry;
matroids; cylindrical algebraic decomposition; quantifier elimination; homotopy continuation; intersection theory.
- Applied algebra, geometry and topology: Chemical reaction networks; algebraic statistics and phylogenetics; image analysis; identifiability problems; persistent homology; point group determination.