Date:

Location:

CB 114

Speaker(s) / Presenter(s):

Lei Xue, University of Michigan

KOI Combinatorics Lectures

Speaker: Lei Xue, University of Michigan

Title: A proof of Grünbaum's Lower Bound Conjecture for polytopes, lattices, and strongly regular pseudomanifolds

Abstract:

In 1967, Grünbaum conjectured that any d-dimensional polytope with d+s ≤ 2d vertices has at least φ_{k}(d+s, d) = {d+1 choose k+1} + {d choose k+1} - {d+1-k \choose k+1} \] k-faces. In the talk, we will prove this conjecture and discuss equality cases. We will then extend our results to lattices with diamond property (the inequality part) and to strongly regular normal pseudomanifolds (the equality part). We will also talk about recent results on d-dimensional polytopes with 2d+1 or 2d+2 vertices.

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