Secants of Grassmannians and Lagrangian Grassmannians
Ada Boralevi

The Lagrangian Grassmannian LG(n,2n) is a projective variety parametrizing dimension n isotropic subspaces of a symplectic complex vector space of double dimension 2n. In this talk I will talk about a joint work with Jarek Buczyinski, where we computed the dimensions of the 3rd and 4th secant varieties of LG(n,2n). Our result is an application of the classic Terracini Lemma, and it fits nicely with the (presently still) canjectural classification of defective secants to ordinary Grassmannians.