PhD Defense: AmirHosein Sadeghimanesh

Title: Algebraic tools in the study of Multistationarity of Chemical Reaction Networks

Abstract:

This thesis consists of three parts: In the first part, we studied how Grӧbner bases and binomiality of the steady state ideal behave with respect to the addition or removal of intermediate species to a reaction network. After gaining a knowledge about binomiality of networks with intermediates in the first part, the second part studies multistationarity of reaction networks with intermediates and that have a core binomial network. The last part concerns the use of Kac-Rice formulas to study and divide the parameter region of a reaction network according to the number of steady states. A nice implication of this work is the definition of a measure of robustness for multistationarity.