Algebra and Algebraic Geometry Seminar - Elise Walker - Newton-Okounkov bodies of chemical reaction networks
Title: Newton-Okounkov bodies of chemical reaction networks
Abstract: This talk introduces a new application of Newton-Okounkov body theory to the study of chemical reaction networks. An important invariant of a chemical reaction network is its maximum number of positive steady states, which is realized as the maximum number of positive real roots of a parametrized polynomial system. This talk introduces a new upper bound on this number, namely the `Newton-Okounkov body bound' of a chemical reaction network. Explicit examples demonstrate that the Newton-Okounkov body bound of a network gives a good upper bound on its maximum number of positive steady states. This Newton-Okounkov body bound is related to another upper bound, namely the mixed volume of a chemical reaction network. The Newton-Okounkov body often achieves better bounds than the mixed volume.