Algebra and Algebraic Geometry Seminar - Elise Walker - Newton-Okounkov bodies of chemical reaction networks

Description

Speaker: Elise Walker (TAMU)

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.

Zoom Link: https://mcmaster.zoom.us/j/97261230720?pwd=K3BBWmhWZ1BWYTN2cFByajVOcVozQT09

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