Research

Preprints

• Dimension and degeneracy of solutions of parametric polynomial systems arising from reaction networks with Elisenda Feliu and Beatriz Pascual-Escudero (2023).
• 3D genome reconstruction from partially phased Hi-C data with Diego Cifuentes, Jan Draisma, Annachiara Korchmaros and Kaie Kubjas (2023).

Ongoing projects

• Detecting and precluding toricity in reaction network theory
• Generalized polyhedral homotopies and tropical steady state bounds

Mathematical interests

• 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.