Welcome

I am a fifth-year Ph.D. student in Mathematics at the University of Wisconsin–Madison, originally from Concón, Chile. My research lies at the intersection of Dynamical Systems and Mathematical Biology. I work under the direction of Gheorghe Craciun, studying chemical reaction network theory.

Reaction networks are a versatile class of dynamical models that arise in fields such as biochemistry, population dynamics, and epidemiology. These models often lead to systems of polynomial differential equations with unknown parameters. My work focuses on understanding the global behavior of these systems from their structural properties, rather than specific parameter values.

In particular, I aim to translate and extend foundational ideas from mass-action kinetics to generalized Lotka–Volterra systems, with an emphasis on questions of global stability and permanence.

I am also interested in other fundamental questions in the field. For example, I explore extensions of the theory of complex-balanced systems using tools like the Disguised Toric Locus, and I am working toward a more practical understanding of Absolute Concentration Robustness (ACR) in biochemical systems.