Jan Kotrbaty (Charles University)

Title: A Generalization of Godbersen's Conjecture

Abstract: 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 about 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 discuss the connection of the conjectured inequality to the Alesker product of smooth valuations and the intersection product of polytopes introduced recently by Wannerer.

Hybrid seminar** at UdeM, Pavillon André-Aisenstadt, room 5183

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https://umontreal.zoom.us/j/89528730384?pwd=IF10Cg8C0YfogaBlL6F1NboPaQvAaV.1

Meeting ID: 895 2873 0384

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