Gleb Pogudin - Realizability of differential equations and rationality of algebraic varieties

mardi 25 nov. 2025, 14:00 → 15:00 Europe/Paris

435 (UMPA)

Realizability problem is an old question in control theory asking if a given nonlinear differential equation can be realized as in input-output relation of a dynamical system. Many different versions of the question depending on the considered classes of differential equations and dynamical systems have been considered. 

For rational dynamical systems without external inputs, a surprising characterisation was obtained in 1993 by Forsman: an equation is realisable if and only if it defines a unirational algebraic hypersurface. This interplay between differential equations and algebraic geometry has been recently used to extend this result to a larger class of models involving external inputs. I will describe these recent developments and discuss some natural open questions.

The talk is based on the joint work with Dmitrii Pavlov.