The double Cayley Grassmannian is a unique smooth equivariant completion with Picard number one of the symmetric space G_2, and it parametrizes eight-dimensional isotropic subalgebras of the complexified bioctonions. We show the rigidity of the double Cayley Grassmannian under Kahler deformations. This is a joint work with K.D. Park

I will outline an ongoing project that attempts to understand symplectic geometry behind the positive integer solutions of the Diophantine equation  a1^2+a2^2+ ...+an^2=na1a2...an.

The double Cayley Grassmannian is a unique smooth equivariant completion with Picard number one of the 14-dimensional exceptional complex Lie group G2, and it parametrizes eight-dimensional isotropic subalgebras of the complexified bioctonions. From the Kodaira-Spencer deformation theory, for the local deformation rigidity of complex structures of a compact complex manifold it suffices to prove the vanishing of the first cohomology group of its tangent bundle. We can prove that the double Cayley Grassmannian is locally rigid using the Borel–Weil–Bott theorem and the Koszul complex associated with a description as the zero locus of a general global section of the rank seven vector bundle on the 21-dimensional spinor variety.

TBA