Johannes Kepler Symposium für Mathematik

Im Rahmen des Johannes-Kepler-Symposiums für Mathematik wird Dr. Georg Regensburger, Institute for Algebra, JKU Linz, am Wed, Nov. 22, 2017 um 17:15 Uhr im HS 13 einen öffentlichen Vortrag (mit anschließender Diskussion) zum Thema "Positive steady states and solutions of polynomial systems with real exponents" halten, zu dem die Veranstalter des Symposiums,

O.Univ.-Prof. Dr. Ulrich Langer,
Univ.-Prof. Dr. Gerhard Larcher
A.Univ.-Prof. Dr. Jürgen Maaß, und
die ÖMG (Österreichische Mathematische Gesellschaft)

hiermit herzlich einladen.

Series B - Mathematical Colloquium:

The intention is to present new mathematical results for an audience interested in general mathematics.

Positive steady states and solutions of polynomial systems with real exponents

Reaction networks with mass action kinetics give rise to polynomial ODE
systems. Chemical reaction network theory (CRNT) provides statements
about uniqueness, existence, and stability of positive steady states for
all rate constants and initial conditions depending on the underlying
network structure alone. In terms of polynomial equations, they
guarantee existence and uniqueness of positive solutions for all
positive parameters.

We first survey several results from CRNT, emphasizing the consequences
for polynomial equations with real and symbolic exponents and addressing
computational aspects. Then we describe an extension to generalized mass
action systems where reaction rates are allowed to be power-laws in the
concentrations. In this setting, uniqueness and existence for all
parameters additionally depend on sign vectors of related vector
subspaces. We also illustrate our results with an implementation in the
computer algebra system Maple. This is joint work with Stefan Müller.
Finally, we discuss an interpretation of the results as a first partial
multivariate generalization of the classical Descartes’ rule for
positive roots of univariate polynomials. This is joint work Carsten
Conradi, Alicia Dickenstein, Elisenda Feliu, Stefan Müller, and Anne Shiu.