Hemisystems of the Hermitian surfaces
[TMCSC]
July 19, 2019 15:00-16:00
四川大学东三教学楼 246
![[lecture]0719Qing Xiang.jpg](http://tianyuan.scu.edu.cn/upload/default/20190712/%5Blecture%5D0719Qing%20Xiang.jpg "[lecture]0719Qing Xiang.jpg")
SPEAKER
向青 (University of Delaware)
ABSTRACT
Hemisystems were first introduced by Segre in 1955. For about fifty years, the only known hemisystem was the one constructed by Segre in H(3; 3 ²); and it was conjectured that no more hemisystems could be found. In 2005, Cossi-dente and Penttila constructed a hemisystem of H(3; q ²) for each odd prime power q. In this talk, we survey the known constructions of hemisystems in H(3; q ²) and also give the details on a recent construction of hemisystems of H(3; q ²) for prime powers q congruent to 3 modulo 4 by using cyclotomic classes. Important ingredients in the proofs are Gauss sums/Gauss periods. This talk is based on joint work with John Bamberg, Koji Momihara and Melissa Lee.
ORGANIZERS
洪绍方（四川大学）
寇 辉（四川大学）
连 增（四川大学）
SUPPORTED BY
国家天元数学西南中心
四川大学数学学院