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Applications of numerical algebraic geometry

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Many models can be written as systems of polynomial equations. For time-dependent ODE models, such as those in biological signalling pathways or cell-cell interactions, it is desirable to compute the steady-states. Sometimes the systems are too large to solve by hand, which motivates the use of techniques from computational algebraic geometry. Rather than starting from an initial guess using Newton’s method, one can numerically approximate all the isolated steady-states using numerical algebraic geometry. I will present three different case studies that extend numerical algebraic geometry methods to study different problems arising in biology. Specifically, I will focus first on comparing models with steady-state data, then computing regions of the parameter space that give different numbers of stable real steady-states, and, time permitting, developing an algorithm for sampling points on a real algebraic variety (such as those arising in configuration spaces of molecules) to run topological data analysis.

This talk is part of the CCIMI Seminars series.

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