Mini-course on bifurcation currents

Speaker:  Matias Carrasco (Aix Marseille Université)

Abstract:

We will study bifurcations within holomorphic families of polynomials or rational maps by
mean of ergodic and pluripotential theoretic tools. Around 2000, a decisive achievement
was made by DeMarco: in any holomorphic family of rational maps, the bifurcation locus
is the support of a (1, 1) closed positive current Tbif admiting the Lyapunov exponent
function as a global potential. In the recent years, several authors have investigated the
geometry of the bifurcation locus using the current Tbif . We shall present here some of the
these important results. The course will be informal and we will pay particular attention
to the basics of the theories involved: complex analysis in several variables, differentiable
forms and currents.