3 événements

• Mathématiques de l’apprentissage

Lundi 11 février 12:30-13:30 - Stéphane Puechmorel - ENAC

Ouverture du GdT Géométrie, Topologie et Statistique

Résumé : This opening session for the working group on topology, geometry and statistics will be a non-technical introduction to information geometry, a topic that has recently gained a lot of attention.
The starting point will be the Cramer-Rao bound in estimation theory and its expression with the so-called Fisher information. The main idea behind information geometry is that Fisher information may be viewed as a local inner product, which in turn allows to endow the parameter space of a parameterized model with a Riemannian structure. Through the example of the univariate normal distribution family, the importance of the geometry arising from this structure will be demonstrated. In particular, the notions of geodesic distance between densities, curvature and barycenters will be introduced.
Switching to the natural exponential family illustrates the need for new objects called $\alpha$-connections, that have a simple statistical interpretation.
Finally, the concept of statistical manifolds will be introduced as a natural framework for dealing with objects generalizing the $\alpha$-connections in the exponential case.
PS : details about the next sessions will be posted on this web page.

Lieu : Bâtiment 1R3, salle de conférence du 1er étage (MIP)

• Séminaire d’Analyse Réelle

Lundi 11 février 14:00-15:00 - Blagovest Sendov - Bulgarian Academy of Sciences

Extrem problems in the geometry of polynomials

Résumé : The Geometry of polynomials study the geometric relations, on the complex plane $\mathcal C$, between the zeros of a complex polynomial $p(z)$ and the zeros of its derivative $p’(z)$. The fundamental fact in this field is the

Gauss-Lucas theorem The convex hull $K(p)$ of the zeros of a polynomial $p(z)$ contain the zeros of its derivative $p’(z)$.

The lecture is devoted to some open extreme problems in the geometry of polynomials.

Lieu : Salle 106, bâtiment 1R1

• Homotopie en Géométrie Algébrique

Mardi 12 février -

Semaine ALPE Lundi 11 à Montpellier - pas de séminaire le mardi