Geometry and Dynamics of Discrete Actions

Satellite Conference of the 2026 ICM

Cuernavaca, Mexico, june 16th to 20th, 2026

Brief Description:

The study of discrete actions of groups and semi-groups plays a central role in geometry and dynamics. This originates in the pioneering work of H. Poincaré over a century ago, studying solutions of certain differential equations on the complex line. The study of discrete group-actions has played for decades a major role in complex geometry and holomorphic dynamics; and so, does iteration theory of rational maps and endomorphisms of complex spaces.

The study of discrete group and semigroup actions remains at the heart of several fields, from complex geometry and holomorphic dynamics to moduli spaces, geometric topology and more. Active research continues in higher Teichmüller theory, dynamical moduli spaces, geometric structures on character varieties, and connections to physics through string theory and quantum geometry.

Main Topics:

• Endomorphisms of projective spaces. Fatou sets.
• Real and complex hyperbolic geometry.
• Kleinian groups and discrete group actions on complex manifolds.
• Moduli spaces of dynamical systems and representations.
• Topology and dynamics of character varieties.
• Teichmüller theory.
• Complex representations of fundamental groups.
• Transcendental Dynamics.