Colloquium Maths-Info mardi 5 juin 2018
Salle 2B101, bâtiment Copernic, Upem Cité Descartes
Contact : Matthieu Fradelizi
Titre : Bezout Inequality for Mixed volumes.
Résumé : In this talk we will discuss an analog of Bezout inequality for mixed volumes of convex bodies. We will start with a general introduction to the theory of mixed volumes and its connections to algebraic geometry, in particular to the Bezout inequality.We will present a conjecture the the new Bezout inequality for mixed volumes characterizes simplices. 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.
Titre : Nearly orthogonal vectors.
Résumé : How to arrange d+k vectors in R^d so that they are as close to orthogonal as possible ? We show a connection of this problem to an optimization problem over isotropic measures. Using this connection, we solve the problem for k=1, 2, 3, 7 and 23. Joint work with Chris Cox.