## 1 événement

• Séminaire d’Analyse Réelle

### Lundi 9 juillet 2018 14:00-15:00 - Artem Zvavitch - Kent State University

Bezout Inequality for Mixed volumes

Résumé : In this talk we will discuss the following analog of Bezout inequality for mixed volumes : for $2 \le r \le n$,
$$V(P_1,…,P_r,\Delta^n-r) V_n(\Delta)^r-1} \le \prod_i=1}^r V(P_i,\Delta^n-1}).$$
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 $P_1,…, P_r$ are convex bodies in $R^n$. We will present a conjecture that if the above inequality is true for all convex bodies $P_1,…, P_r$, 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.

Lieu : Bâtiment 1R1, salle 106