61 Probability Encounters, In honour of Sergey Bobkov

Maud Szusterman: Bezout inequality with mixed volumes : is the simplex the only minimizer?

31 mai 2023, 11:10

45m

Paul Sabatier University, Toulouse

Orateur

Maud Szusterman

Description

I. Soprunov and A. Zvavitch have shown some mixed volume inequalities for the simplex, which translate algebraic inequalities known as Bezout inequalities. Together with C. Saroglou, they have proven in 2018 that this family of inequalities characterizes the simplex among all polytopes, and conjecturally the characterization would hold among all convex bodies in R^n. These three authors have shown the conjecture holds true in dimension 3, we provide an alternative proof, and indicate partial results in dimension 4.