Georg Regensburger (Univ. Kassel): Reaction networks and positive solutions to systems of polynomial equations with real exponents
Abstract:
Many dynamical systems used in chemistry and biology can be represented as reaction networks with generalized mass-action kinetics. The study of positive equilibria in these systems leads to generalized polynomial equations with real exponents and positive parameters. In this talk, we first provide a brief introduction to reaction networks. Then, we describe some of our results on positive equilibria that are determined by the underlying graph.
In the second part of the talk, we discuss a recent framework for arbitrary systems of generalized polynomial equations with positive variables and parameters for each monomial. The relevant geometric objects in the problem are a polytope arising from the coefficients and two subspaces representing differences and dependencies of the exponents. We demonstrate our approach with several examples from fewnomial theory.
Mit freundlichen Grüßen,
Prof. Dr. Georg Regensburger (AG AADM)