**Mihai-Marius Tibar**

University of Lille-1, France

November 3, 2011

**Betti bounds of polynomials**:
We initiate a classication of polynomial functions $f: \mathbb C^n \to \mathbb C$ of degree $d$ having the top Betti number of the general bre close to the maximum. We nd a range in which the polynomial must have isolated singularities and another range where it may have at most one line singularity of Morse transversal type. Our method uses deformations into particular pencils with non-isolated singularities. This is a joint work with Dirk Siersma.