Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
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Meeting ID: 915 4733 5974
A simplicial complex on $n$ vertices is $s$-neighborly if it has the same $(s − 1)$-skeleton as the $(n − 1)$-simplex on the same vertex set. While a $(d-1)$-dimensional sphere with $n>d+1$ vertices cannot be more than $\lfloor d/2\rfloor$-neighborly, $\lfloor d/2\rfloor$-neighborly $(d-1)$-dimensional spheres with $n$ vertices do exist. How many such neighborly spheres are there? We will present a recent construction showing that for $d\geq 5$, there are at least $2^{\Omega(n^{\lfloor (d-1)/2\rfloor})}$ distinct combinatorial types of neighborly spheres.
Joint work with Hailun Zheng.