Date: Friday, January 12, 2018
Location: 4088 East Hall (4:10 PM to 5:00 PM)
Title: A lower bound theorem for centrally symmetric simplicial polytopes
Abstract: An important invariant in the study of face numbers of simplicial dpolytopes is the gvector. The generalized lower bound theorem states that g_i is nonnegative for any simplicial polytope and characterizes the case of equality. Much less is known for centrally symmetric polytopes. A seminal work is established by Stanley thirty years ago, where he proved that for any centrally symmetric simplicial dpolytope P with d at least 3 and i between 1 and d/2, we have g_i(P) \geq \binom{d}{i}\binom{d}{i1}.
In this talk, I will introduce the rigidity theory of frameworks, and show how to apply this machinery to give a characterization of centrally symmetric dpolytopes with which satisfy g_2=\binom{d}{2}d. This is joint work with Steve Klee, Eran Nevo and Isabella Novik.
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Speaker: Hailun Zheng
Institution: University of Michigan
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