Some geometric applications of Hodge theory (Talks in Chile and Montreal)

Hodge theory is a subject of both interest in it's own right and as a tool for studying geometric questions. This talk will be mainly concerned with some of the history and uses of Hodge theory: how did it originate and what are some of the ways it helps to address problems in geometry, especially algebraic geometry? Our discussion of both the early history and uses of Hodge theory will be selective, not comprehensive.