Constructions of $m$-ovoids of Symplectic Polar Spaces
报告题目(Title)：Constructions of $m$-ovoids of Symplectic Polar Spaces
报告人(Speaker)：向 青教授 (南方科技大学)
地点(Place)：腾讯会议 ID：496 838 544
时间(Time)：2021年4月8日（周四）下午15:30-16:30
邀请人(Inviter)：吕本建, 王恺顺
报告摘要
An $m$-ovoid in the symplectic polar space $W(2r-1,q)$ is a set ${\mathcal M}$ of points such that every maximal of $W(2r-1,q)$ meets ${\mathcal M}$ in exactly $m$ points. A 1-ovoid in $W(2r-1,q)$ is simply called an ovoid. Ovoids in $W(2r-1,q)$ (and more generally in any classical polar space) were first defined by Thas (1981). The concept of an ovoid was later generalized to that of an $m$-ovoid by Thas (1989) and Shult/Thas (1994).
We discuss a new method for constructing $m$-ovoids in the symplectic polar space $W(2r-1,q)$ from cyclotomic strongly regular graphs constructed in a paper by Brouwer, Wilson and Xiang (1999). Using this method, we obtain many new $m$-ovoids which can not be derived by field reduction. This talk is based on joint work with Tao Feng and Ye Wang, both of Zhejiang University.
