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Reconstruction of polytopes and Kalai's conjecture on reconstruction of spheres

Algebra & Discrete Mathematics

Speaker: Joseph Doolittle, TU Graz
Location: Zoom
Start time: Fri, Nov 4 2022, 3:10PM

A famous theorem in polytope theory states that the combinatorial type of a simplicial polytope is completely determined by its facet-ridge graph. This celebrated result was proven by Blind and Mani in 1987, via a non-constructive proof using topological tools from homology theory. Shortly after, Kalai gave an elegant constructive proof, requiring exponential time to compute. In their original paper, Blind and Mani asked whether their result can be extended to simplicial spheres, and a positive answer to their question was conjectured by Kalai. The purpose of this talk is to show that Kalai’s conjecture holds in the particular case of Knutson and Miller’s spherical subword complexes, a family of simplicial spheres of importance in the study of Gröbner geometry of Schubert varieties.

This talk is based on joint work with Cesar Ceballos.