Title:SL(n) Contravariant Tensor Valuations
Speaker:李晋（Shanghai University）
Time: 05/29 (Thursday), 10:00-11:30
Venue: Gewu Building, Room 315
Abstract :
Valuations are scissors congruence invariants that play fundamental roles in Hilbert's third problem. In this talk, I will present a complete classification of SL(n) contravariant, p-order tensor valuations on convex polytopes in \mathbb{R}^n for n ≥ p without imposing additional assumptions, particularly omitting any symmetry requirements on the tensors. Beyond recovering known symmetric tensor valuations, our classification reveals asymmetric counterparts associated with the cross tensor and the Levi-Civita tensor. Additionally, some Minkowski type relations for these asymmetric tensor valuations will be represented, extending the classical Minkowski relation of surface area measures.
