Abstracts
for the Seminar

Fall 2018

**Speaker: **Hailun Zheng, University of Michigan

**Title: ** An upper theorem for odd-dimensional flag normal pseudomanifolds

**Time:** 2:30 PM, Monday, October 15, 2018

**Place:** Malott 206

**Abstract:** A simplicial complex is flag if all of its minimal non-faces have cardinality two. The celebrated upper bound theorem states that among all simplicial (d-1)-spheres with n vertices, neighborly spheres simultaneously maximize all the face numbers. On the other hand, the sharp upper bounds on the face numbers of flag spheres are less well-understood. Lutz and Nevo conjectured that for flag (2m-1)-spheres with n vertices (m>1), the join of m circles of length as close as possible is the unique maximizer of all face numbers.

In this talk, I will survey recent results on this topic and prove the Lutz-Nevo conjecture for the edge number in the class of flag normal pseudomanifolds. .

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