For the talk A Geometric perspective on machine Learning given by Professor Partha Niyogi (1967-2010) , the video is here. There is another video lecture give by Partha Niyogi about Geometric Methods and Manifold Learning here.
The subject was manifold learning:
Given a collection of (unlabelled) data inhabiting some high dimensional space, can you determine whether they actually lie on some lower dimensional manifold in this space ?
This talk was a great window into an area of machine learning with strong geometric connections, an area where geometers could profitably play and make useful contributions.