IMAS   23417
INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
From chemical reaction networks to Descartes' rule of signs
Autor/es:
A. DICKENSTEIN
Lugar:
Villa de Lyva
Reunión:
Workshop; CIMPA School on Real Algebraic Geometry; 2014
Institución organizadora:
CIMPA
Resumen:
In
the context of chemical reaction networks with mass-action and other rational
kinetics, a major question is to preclude or to guarantee multiple positive
steady states. I will explain this motivation and I will present
necessary and sufficient conditions in terms of sign vectors for the
injectivity of families of polynomials maps with arbitrary real exponents
defined on the positive orthant. These conditions extend existing injectivity
conditions expressed in terms of Jacobian matrices and determinants, obtained
by several authors. In the context of real algebraic geometry, this approach
can be seen as the first partial multivariate generalization of the classical
Descartes' rule, which bounds the number of positive real roots of a univariate
real polynomial in terms of the number of sign variations of its coefficients.
This is joint work with Stefan Müller, Elisenda Feliu, Georg
Regensburger, Anne Shiu and Carsten Conradi. I will also present some further
advances in this multivariate generalization obtained in collaboration with
Frédéric Bihan.