BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Elisenda Feliu (University of Copenhagen) DTSTART:20230209T160000Z DTEND:20230209T163000Z DTSTAMP:20260421T124243Z UID:MoRN/63 DESCRIPTION:Title: On the generic dimension and nondegeneracy of steady states of reaction netw orks\nby Elisenda Feliu (University of Copenhagen) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nIn the context of ( bio)chemical reaction networks\, the dynamics of the concentrations of the chemical species over time are often modelled by a system of parameter-de pendent ordinary differential equations\, which are typically polynomial o r described by rational functions. The dynamics of a reaction network are also often constrained into invariant linear subspaces called stoichiometr ic compatibility classes. The study of the steady states of the system tr anslates then into the study of the positive solutions to a parametric pol ynomial system. The set of positive solutions lives inside a complex algeb raic variety and hence tools from algebraic geometry naturally find applic ation in this field. \n\nIn this talk I will discuss recent results addres sing the following questions: What is the expected dimension of the algebr aic variety of steady states? Can the dimension be "wrong" in an open set of parameters? Under what conditions is the intersection of the algebraic variety of steady states with the stoichiometric compatibility classes gen erically finite? \n\nThese are fundamental questions to understand the alg ebraic nature of the objects under study\, and have been previously brough t up in the study of reaction networks\, for example in the context of we akly reversible reaction networks. Additionally\, knowing the answer to th ese questions in advance is often necessary to be able to apply the mathem atical machinery coming from complex algebraic geometry. \n\nThis talk is based on join work in progress with Oskar Henriksson and Beatriz Pascual-E scudero.\n LOCATION:https://researchseminars.org/talk/MoRN/63/ END:VEVENT END:VCALENDAR