Séminaire Doctorants
organisé par l'équipe DOCT
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Marthe Guillermit
Volumes of moduli spaces of hyperbolic surfaces
10 juin 2026 - 16:30Salle de séminaires IRMA
Over the past decade, the study of the asymptotic growth of volumes has yielded numerous results on the length spectrum and on the spectrum of the Laplacian of typical high-genus surfaces. A more precise understanding of the expansion of the volumes allows us to figure out what happens to the counting functions of closed geodesics of length less than L at the threshold square-root of g. -
Mabrouk Ben Jaba
Some Historical Optimization Problems Revisited Through Optimal Control Theory
18 juin 2026 - 16:30Salle de conférences IRMA
The aim of this talk is to explore several historical optimization problems together, namely Dido’s problem and the brachistochrone problem, by adopting an optimal control perspective. We start by introducing optimal control theory. This mathematical discipline consists in determining the best way to influence a dynamical system through a control or input so as to steer it toward a target state [control], while minimizing or maximizing a given cost functional [optimal]. Optimal control theory is used in a wide range of fields, including aerospace engineering (rocket trajectory optimization), finance (optimal portfolio management), and biology (population management). We focus on the case where a dynamical system is described by ordinary differential equations and we present Pontryagin’s Maximum Principle. An outline of the proof, aimed at providing insight into this principle, will also be given. Finally, we apply this framework to the historical problems mentioned above.