A generalization of Godbersen's conjecture

Jan Kotrbatý 

The long-standing Godbersen's conjecture asserts that the Rogers-Shephard inequality for the volume of the difference body is refined by an inequality for the mixed volume of a convex body and its reflection in the origin. The conjecture is known in several special cases, notably for anti-blocking convex bodies. In this talk, we will propose a generalization of Godbersen's conjecture that refines Schneider's generalization of the Rogers-Shephard inequality to higher-order difference bodies and we will show it is true for anti-blocking convex bodies. We will also present two equivalent algebraic formulations of the conjectured inequality.