# Colloquium abstracts

**Chaitanya Senapathi**

TIFR

November 21, 2013

**Morse theory on the space of paths in Homogeneous Space**: Homotopy connectedness theorems for complex submanifolds of flag manifolds $G/P$ (referred to as theorems of Barth-Lefschetz type) have been established by a number of authors. Morse Theory on the space of paths leads to an elegant proof of homotopy connectedness theorems for complex submanifolds of Hermitian symmetric spaces. In this talk we sketch how to extend this proof to a larger class of flag manifolds which include $G/B$ where $G$ is simple and $B$ is a Borel subgroup.