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Realization space of projection areas of convex bodies

Speaker：

Shouda Wang (Princeton University)

Time：

Wed., 11:00 am–12:00

Dec. 31, 2025

Venue：

B725, Shuangqing Complex Building A

Abstract:

Fix a 4-dimensional convex body and consider the areas of its orthogonal projections onto the six coordinate planes. This associates to each convex body a 6-tuple of nonnegative numbers. I will explain a surprising connection: the set of all such 6-tuples coincides with the set of all 4-by-4 symmetric matrices with nonnegative entries, zero diagonal, and Lorentzian signature. And in addition, this set is also equal to the Grassmannian over a certain triangular hyperfield. This talk is based on joint work with Huang, Huh, Michałek, and Wang.