" Morse theory for Harmonic forms"
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
of closed 1-forms. I will also describe a beautiful Theorem of Calabi,
a topological characterization of harmonic 1-forms.