Wednesday 11 March 2026, from 2 pm in Room U6-41 (U6 Building - Piazza dell'Ateneo Nuovo 1, Milano), Fabrizio Bianchi (University of Pisa) and Alessandro Minuzzo (University of Parma) will give the following talks
Speaker: Fabrizio Bianchi
Title: Holomorphic motions of Julia sets: dynamical stability in one and several complex variables
Abstract: We discuss the stability of holomorphic dynamical systems under perturbation. In dimension 1, the theory is now classical and is based on works by Lyubich, Mané-Sad-Sullivan, and DeMarco. I will review this theory and present a recent generalisation valid in any dimension. Since classical 1-dimensional techniques no longer apply in higher dimensions, our approach is based on ergodic and pluripotential methods.
Speaker: Alessandro Minuzzo
Title: On the Rational Hyperbolicity Problem
Abstract: We find counterexamples to a conjecture by Grove, Wilking and Yeager. The conjecture states that if M is a closed, simply connected G-manifold, whose quotient M/G is a hyperbolic polygon, then M is rationally hyperbolic. These counterexamples also disprove an analogous conjecture for polar actions by Grove and Ziller and several other questions concerning the rational homotopy of manifolds with symmetry. On the other hand, it is interesting to look for vast classes of G-manifolds verifying the above conjectures. In pursuing this investigation, we prove that if M is a closed and simply connected Riemannian manifold, admitting a variationally complete isometric G-action, such that either a principal isotropy is connected or a principal orbit is simply connected, then M is rationally elliptic if and only if M/G is flat. This is a joint work with Prof. M. Radeschi and Prof. R. Mendes.
All interested are invited to participate
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