## Holomorphic Dynamics and Our Research

Dynamical systems play a key role all across mathematics: they are of fundamental importance in diverse applications ranging from celestial mechanics and population biology to economy and mathematical finance, and within theoretical mathematics they are closely connected to geometry, topology, and other branches of current research. One of the most developed aspects of dynamical systems is *holomorphic dynamics*, that is the iteration of complex analytic maps. This research area has been credited as “*a lively and important branch of mathematics straddling the traditional borders between pure and applied areas*¹ ”. One of the particularly attractive features of holomorphic dynamics is that it closely connects to deep methods and tools in as diverse areas as geometry (for instance hyperbolic geometry), number theory, algebra, topology, general dynamics, and more; it has attracted many top-notch researchers, including several Abel laureates and Fields medalists (Artur Avila, Curt McMullen, John Milnor, Stanislav Smirnov, William Thurston, Jean-Christophe Yoccoz, …).

Below, we list the research areas in which our group is most active.

¹ in the citation to Dennis Sullivan upon being awarded the National Medal of Science in 2004.