Thirty-Third Annual Victorian Algebra Conference, Sydney, Australia, 2015

Register for: VAC33

Details of talk

TitleSchubert Calculus and Finite Geometry
PresenterJon Xu (The University of Melbourne)
Author(s)Mr Jon Xu

Ovoids in projective space were first defined by Jacques Tits in 1962 after the
realisation that the Suzuki groups have a natural action on sets of points
share many geometric properties with elliptic quadrics. In 1972, Jef Thas gave
definition of ovoids for polar spaces. The study of ovoids is an active field
research in finite geometry, and there are many open problems.

Schubert calculus involves translating geometric properties to a Schubert
variety and studying its cohomology. Schubert varieties are one of the most
well-studied complex projective varieties in the literature.  

It is known that some non-degenerate hyperplane sections of Schubert varieties
are ovoids. Therefore, it is natural to ask: what are the necessary and
sufficient conditions for hyperplane sections of Schubert varieties to be
ovoids? I will talk about the current progress on this problem.