Orateur
Description
In the 1980’s, William Thurston obtained his celebrated characterization of post-critically finite rational maps. This result laid the foundation of such a field as Thurston's theory in holomorphic dynamics, which has been actively developing in the last few decades. One of the most important problems in this area is the characterization question, which asks whether a given topological map is equivalent (in a certain dynamical sense) to a holomorphic one. The result of W. Thurston and further developments allow us to answer this question quite effectively in the setting of (postcritically finite) maps of finite degree, and it has numerous applications for the dynamics of rational maps.
A similar question can be formulated for the maps of infinite degrees (i.e., in the transcendental setting), for instance, for entire or meromorphic postsingularly finite maps. However, the characterization problem becomes significantly more complicated, and the complete answer in the transcendental case is still not known. The first breakthrough in this area was achieved by J.H. Hubbard, D. Schleicher, and M. Shishikura, who provided a topological characterization of postsingularly finite exponential maps. Although this family is relatively simple, their result required the development of entirely new techniques.
In my talk, I am going to introduce key notions of Thurston's theory in the transcendental setting. I will present a result demonstrating that a variant of Thurston's theorem applies to a broad class of transcendental maps, many of which are not defined by simple explicit formulas. If time allows, I will also briefly discuss a "relative" version of Thurston's theorem, which holds in full generality for both finite and infinite degree cases.
