Séminaires : Séminaire d'Analyse Fonctionnelle

Equipe(s) : af,
Responsables :E. Abakoumov - D. Cordero-Erausquin - G. Godefroy - O. Guédon - B. Maurey - G.Pisier
Email des responsables :
Salle : salle 13 - couloir 15-16 - 4ème étage
Adresse :Campus Pierre et Marie Curie
Le Jeudi à 10h30 -  IMJ-PRG - 4 place Jussieu - 75005 PARIS

Orateur(s) Artem Zvavitch - Kent,
Titre Bezout Inequality for Mixed volumes
Horaire10:30 à 17:40
In this talk we will discuss the following analog of Bezout inequality for mixed volumes: $
V(P_1,\dots,P_r,\Delta^n-r)V_n(\Delta)^r-1\leq \prod_i=1^r V(P_i,\Delta^n-1)\ \text for 2\leq r\leq n.
$ We will briefly explain the connection of the above inequality to the original Bezout inequality and show that the inequality is true when $\Delta$ is an $n$-dimensional simplex and $P_1, \dots, P_r$ are convex bodies in $\mathbb R^n$. We will present a conjecture that if the above inequality is true for all convex bodies $P_1, \dots, P_r$, then $\Delta$ must be an $n$-dimensional simplex. We will show that the conjecture is true in many special cases. Finally, we connect the inequality to an inequality on the volume of orthogonal projections of convex bodies as well as present an isomorphic version of the inequality.
Sallesalle 13 - couloir 15-16 - 4ème étage
AdresseCampus Pierre et Marie Curie