Abstract:

In 1969 E. Calabi asked the following question: "Does there exist Morse theory of harmonic 1-forms?" In the lecture I will describe a recent theorem (joint work with G. Katz and J. Levine), answering the question of E. Calabi. Most of the lecture will consist in reminding the main principles of the Morse critical point theory of functions and the Novikov critical point theory of closed 1-forms. I will also describe a beautiful Theorem of Calabi, which gives a topological characterization of harmonic 1-forms.