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 φk(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.
Event Series: