Abstract

In this talk, we will discuss the problem of determining the generic root counts of parametrisedpolynomial systems over an algebraically closed field.We wil briefly touch upon the motivation from polynomial system solving, and describe how tropicalgeometry can help in this task. We will give a brief glimpse on the algebraic geometry behind thetropical intersection product, and discuss various strategies how the latter can be computed. Weconclude the talk by highlighting applications to chemical reaction networks, coupled oscillators,and graph rigidity.