BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Oskar Henriksson (University of Copenhagen) DTSTART:20231130T163000Z DTEND:20231130T170000Z DTSTAMP:20260421T123923Z UID:MoRN/84 DESCRIPTION:Title: Fi nding all steady states with tropical geometry\nby Oskar Henriksson (U niversity of Copenhagen) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nThe point of departure of this talk is the follow ing seemingly simple question: Suppose we are given a reaction network wit h (generalized) mass action kinetics\, and a choice of rate constants and total amounts – how do we find numerical approximations of *all* the pos itive steady states?\n\nOne possible method is to use numerical algebraic geometry to completely solve the steady state equations over the complex n umbers\, and then use interval arithmetic methods to filter out the real p ositive solutions. This approach has the advantage of finding all positive steady states with probability 1 (including unstable ones that would be h ard to find with traditional ODE methods)\, and additionally makes it poss ible to *certify* in the end that all steady states have been found.\n\nIn this talk\, I will outline the basic ideas behind this type of numerical algebraic geometry solvers\, and then describe recent joint work in progre ss with Feliu\, Helminck\, Ren\, Schröter and Telek\, where we use tropic al geometry and matroid theory to determine the so-called *steady state de gree* of a network\, which is needed to ensure efficiency and certifiabili ty.\n LOCATION:https://researchseminars.org/talk/MoRN/84/ END:VEVENT END:VCALENDAR