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SUMMARY:Applications of numerical algebraic geometry - Heather Harrington 
 Oxford
DTSTART:20170210T150000Z
DTEND:20170210T160000Z
UID:TALK69668@talks.cam.ac.uk
CONTACT:Rachel Furner
DESCRIPTION:Many models can be written as systems of polynomial equations.
  For time-dependent ODE models\, such as those in biological signalling pa
 thways or cell-cell interactions\, it is desirable to compute the steady-s
 tates. Sometimes the systems are too large to solve by hand\, which motiva
 tes the use of techniques from computational algebraic geometry. Rather th
 an starting from an initial guess using Newton's method\, one can numerica
 lly approximate all the isolated steady-states using numerical algebraic g
 eometry. I will present three different case studies that  extend numerica
 l algebraic geometry methods to study different problems arising in biolog
 y. 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 th
 ose arising in configuration spaces of molecules) to run topological data 
 analysis.\n\n
LOCATION:MR5 Centre for Mathematical Sciences
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