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SUMMARY:Carles Checa Nualart (University of Copenhagen)
DTSTART:20251106T160000Z
DTEND:20251106T163000Z
DTSTAMP:20260421T124814Z
UID:MoRN/126
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MoRN/126/">A
 n effective criterion for multiple positive solutions of vertical systems<
 /a>\nby Carles Checa Nualart (University of Copenhagen) as part of Seminar
  on the Mathematics of Reaction Networks\n\n\nAbstract\nWe present a crite
 rion for determining when a vertically parametrized polynomial system admi
 ts multiple positive zeros for some parameter values. Our approach is base
 d on the higher deficiency algorithms from chemical reaction network theor
 y. Under certain assumptions\, these algorithms reduce the problem to chec
 king the feasibility of a linear system of equalities and inequalities (po
 lyhedral cones). Our criterion requires that the linear part of the system
  (stoichiometric matrix) has a row reduction whose underlying graph is a f
 orest\, implying a highly structured pattern of zeros\, which is often rea
 lized in steady state varieties. Using the same polyhedral cones\, we also
  provide sufficient conditions to derive connectivity of the parameter reg
 ion yielding multiple positive solutions and to guarantee the existence of
  a pair of distinct nondegenerate positive zeros. This is joint work with 
 Elisenda Feliu.\n
LOCATION:https://researchseminars.org/talk/MoRN/126/
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