Date:	Tue, October 7, 2014
Time:	14:15
Place:	Resnikoff Mathematics Lounge

Abstract: Thurston's characterization theorem for postcritically finite rational maps is an important tool for determining whether a postcritically finite topological branch cover is realized by a rational map; this theorem has been used with great success to produce combinatorial models for large classes of functions (e.g. polynomials). The hypothesis of the theorem requires that no multicurves of a certain type exist, a condition that is typically impossible to check since there may be infinitely many multicurves. We present the Nearly Euclidean Thurston maps, a class of highly nontrivial maps where the geometry of Teichmueller space has been exploited in many cases to prove equivalence to a rational map.