# Jerusalem Mathematics Colloquium

Thursday, 25 June 1998, 4:00 pm

Mathematics Bldg., lecture hall 2

## Dr. Maxim Braverman (The Hebrew University of Jerusalem)

## "Morse theory for multi-valued functions"

** Abstract: **

Any smooth function on a compact manifold has at least 2
critical points: maximum and minimum. The celebrated Morse
inequalities imply that on most manifolds each smooth function
has many more critical points.
For example, any function on the two-dimensional torus has at least 4
critical points (provided those points are non-degenerate).

In 1981, S. Novikov extended the Morse inequalities to
multi-valued functions. In my talk, I'll review the
Morse and Novikov theories and present a generalization
of the Novikov inequalities to multi-valued functions
with non-isolated critical points due to M. Farber and
myself. If the time permits, I'll also discuss some
applications.

Coffee, Cookies at the faculty lounge at 3:30.

List of talks, 1997-98