Qifeng Li, Minimal rational curves on equivariant compactifications of symmetric spaces

Let X be a smooth equivariant compactification of a symmetric space. In this talk, we will discuss when a minimal rational curve on X is the orbit closure of a 1-parameter group. In case the symmetric space is of group type, the answer is positive and moreover the VMRT is the closure of an adjoint orbit. This generalizes a result of Brion and Fu’s on wonderful compactifications to arbitrary equivariant compactifications. This is a joint work with Jun-Muk Hwang.