Milnor set of real polynomials and detection of atypical values (Gabriel Monsalve)

For a polynomial function f in two real variables one defines atypical value as a value such that f  is not a locally trivial fibration. The set of atypical values is named the bifurcation set  of f. It is known that all critical values of f are atypical but not every atypical value is critical as the polynomial f=yx^2+x shows. A study of atypical values started in the late 1990's leads to the discovery of two phenomena at infinity that produce atypical values named vanishing and splitting at infinity. In this seminar we will present the Milnor set of the polynomial f and explore its properties that lead us to an effective detection of atypical values.