Geometry Seminar

Date: January 25, 2019

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Xiaoxian Tan, TAMU

Title: Applying Algebraic Methods in Mathematical Biology

Abstract: Many challenging problems in mathematical biology, for instance, in biochemical reaction networks and phylogenetics, are to solve non-linear polynomial systems. Therefore, methods and tools in algebraic geometry and combinatorics are more applicable and powerful. One typical example is the multistationarity problem: whether a given biochemical reaction network has two or more positive steady states? In this talk, we introduce a simple criterion to determine multistationarity for networks arising from biology and to identify the parameter values for which the given network exhibits multistationarity. For linearly binomial networks, we prove our method is much less expensive than standard real quantifier elimination method in computational algebraic geometry. The two key ideas for improving the efficiency are: 1. whether a given network is linearly binomial can be read off easily from graphs associated to the network. 2. linearly binomial networks have nice algebraic and geometric structures.