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## 第79回 2017年2月3日 14:00〜15:30

Alexander Gavrilyuk（中国科学技術大学）「On tight sets of hyperbolic quadrics」

A set of points $M$ of a finite polar space $\mathcal{P}$ is called tight, if the average number
of points of $M$ collinear with a given point of $\mathcal{P}$ equals the maximum possible value.
In the case when $\mathcal{P}$ is a hyperbolic quadric $Q^+(2n+1,q)$, the notion of tight sets
generalises that of Cameron-Liebler line classes in $PG(3,q)$, whose images under the Klein
correspondence are the tight sets of the Klein quadric $Q^+(5,q)$. Very recently, some new constructions
and necessary conditions for the existence of Cameron-Liebler line classes have been obtained.
In this talk, we will discuss a possible extension of these results to the general case of tight set
of hyperbolic quadrics.