Hemisystems of the Hermitian surfaces
July 19, 2019 15:00-16:00
向青 (University of Delaware)
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.