BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Stefan Müller (University of Vienna) DTSTART:20240425T150000Z DTEND:20240425T153000Z DTSTAMP:20260421T124112Z UID:MoRN/100 DESCRIPTION:Title: F rom reaction networks to "positive algebraic geometry" - and back\nby Stefan Müller (University of Vienna) as part of Seminar on the Mathematic s of Reaction Networks\n\n\nAbstract\nEvery power-law dynamical system (an d hence every polynomial dynamical system) used in chemistry and biology ( for example\, in ecology and epidemiology) and even in economics and engin eering can be written as a reaction network with (generalized) mass-action kinetics. \n\nOver the last 10 years\, we have focused on positive equili bria that are determined by the underlying graph (complex-balanced equilib ria). As one highlight\, we have characterized unique existence (in every invariant set and for all rate constants) using sign vectors of subspaces arising from the stoichiometric coefficients and the kinetic orders.\n\nRe cently\, we have turned to general equilibria\, and we study positive solu tions to parametrized systems of generalized polynomial equations (with re al exponents) in abstract terms. We identify the relevant geometric object s of the problem\, namely the coefficient polytope and the monomial differ ence and monomial dependency subspaces. As our main result\, we rewrite po lynomial equations in terms of binomial equations (on the coefficient poly tope). First applications concern real fewnomial and reaction network theo ry.\n\n(Joint work with Georg Regensburger.)\n LOCATION:https://researchseminars.org/talk/MoRN/100/ END:VEVENT END:VCALENDAR