Abstract The positive Grassmannian Gr 0 k; n is the subset of the real Grassmannian where
all Plücker coordinates are nonnegative. It has a beautiful combinatorial structure as well as …

Gibbs manifolds are images of affine spaces of symmetric matrices under the exponential
map. They arise in applications such as optimization, statistics and quantum physics, where …

We show that every multilinear map between Euclidean spaces induces a unique,
continuous, Minkowski multilinear map of the corresponding real cones of zonoids. Applied …

We show that the multistage stochastic linear problem (MSLP) with an arbitrary cost
distribution is equivalent to an MSLP on a finite scenario tree. We establish this exact …

In this manuscript we study how the tools from polyhedral geometry enlighten the structure of
multistage stochastic programming. More precisely, when the arbitrary random variables of a …

We study a class of semialgebraic convex bodies called discotopes. These are instances of
zonoids, objects of interest in real algebraic geometry and random geometry. We focus on …

Given a linear map on the vector space of symmetric matrices, every fiber intersected with
the set of positive semidefinite matrices is a spectrahedron. Using the notion of the fiber …

In this thesis we study problems that lie at the intersection of convex geometry and algebraic
geometry. The main objects of interest are semialgebraic convex bodies: convex, compact …

Dans cette thèse, nous utilisons les outils de la géométrie polyédrale pour appréhender la
struc-ture de problèmes stochastiques. Plus précisément, lorsque les variables aléatoires de …

Abstract (EN) In recent years, algebraic geometry (both complex and real) has proven to be
useful in numerous applications in optimization, statistics, quantum information, and physics …