Speaker:Timo de Wolff
Abstract: Many defining functions in dynamics are represented by multivariate real polynomials. Under this assumption, key properties of dynamical systems often have an algebraic interpretation such as the question of nonnegativity of real, multivariate polynomials. Nonnegativity is not only a classical question in real algebraic geometry. It can also be tackled via polynomial optimization; a thriving field in the past 25 years. In this talk I present two instances highlighting this connection of polynomial optimization and dynamics, which we investigate in recent and ongoing projects: First, deciding mono- vs. multistationarity in 2- and n-site phosphorylation networks in terms of their kinematic parameters (joint work with E. Feliu, N. Kaihnsa, and O. Y¨ur¨uk). Second, computing Lyapunov functions for polynomial ODE systems (joint work with J. Heuer and N. Rieke). Interestingly, both of these results moreover lead to (different) combinatorial follow-up problems, which I will also briefly explain. This talk is meant as an invitation to the audience to further explore the intersection of polynomial optimization, dynamical systems, and combinatorics