June 5, 2018: To celebrate the arrival of our visiting professors UPE and Bézout Artem Zvavitch and Boris Bukh, Matthieu Fradelizi (LAMA) and Xavier Goaoc (LIGM) are pleased to invite you to attend a Mathematics-Computer Science colloquium in room 2B101 (renovated part of the building Copernic at UPEM).
10:00-11:00: Artem Zvavitch (UPE invited professor and Kent State University)
Title: Bézout Inequality for Mixed volumes
Abstract: In this talk we will discuss an analog of Bézout 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 Bézout inequality. We will present a conjecture that the new Bézout 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.
11h-11h30: coffee break
11:30-12:30 : Boris Bukh (Labex Bézout invited professor and Carnegie Mellon University)
Title: Nearly orthogonal vectors
Abstract: 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.