Skip to content
Texas A&M University

Geometry Seminar

Date: August 26, 2020

Time: 10:00AM - 11:15AM

Location: zoom

Speaker: Anna Seigal, Oxford


Title: Ranks of Cubic Surfaces

Abstract: There are various notions of rank, which measure the complexity of a tensor or polynomial. Cubic surfaces can be viewed as symmetric tensors. We consider the non-symmetric tensor rank and the symmetric Waring rank of cubic surfaces, and show that the two notions coincide over the complex numbers. The results extend to order three tensors of all sizes, implying the equality of rank and symmetric rank when the symmetric rank is at most seven. We then explore the connection between the rank of a polynomial and the singularities of its vanishing locus, and we find the possible singular loci of a cubic surface of given rank. This talk is based on joint work with Eunice Sukarto.