Florestan Martin-Baillon (Cergy-Pontoise University)

Bifurcation currents for families of group representations in higher rank

  • Data: 03 MAGGIO 2022  dalle 14:15 alle 16:00

  • Luogo: Seminario 2 ore 14:15

Finitely generated groups acting on projective spaces are examples of holomorphic dynamical systems which exhibit a variety of different behaviours. We introduce the notion of proximal stability which measures a form of dynamical stability for the action of a holomorphic family of group representations and we will explain how this property can be detected using a bifurcation current on the parameter space of the family. This bifurcation current measure the pluriharmonicity of the top Lyapunov exponent of the family of representation, defined using a random walk on the group.